src/HOL/Tools/numeral_simprocs.ML
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(* Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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   Copyright   2000  University of Cambridge
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Simprocs for the (integer) numerals.
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*)
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(*To quote from Provers/Arith/cancel_numeral_factor.ML:
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Cancels common coefficients in balanced expressions:
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     u*#m ~~ u'*#m'  ==  #n*u ~~ #n'*u'
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where ~~ is an appropriate balancing operation (e.g. =, <=, <, div, /)
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and d = gcd(m,m') and n=m/d and n'=m'/d.
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*)
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signature NUMERAL_SIMPROCS =
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sig
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  val assoc_fold_simproc: simproc
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  val combine_numerals: simproc
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  val cancel_numerals: simproc list
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  val cancel_factors: simproc list
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  val cancel_numeral_factors: simproc list
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  val field_combine_numerals: simproc
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  val field_cancel_numeral_factors: simproc list
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  val num_ss: simpset
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  val field_comp_conv: conv
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end;
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structure Numeral_Simprocs : NUMERAL_SIMPROCS =
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struct
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val mk_number = Arith_Data.mk_number;
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val mk_sum = Arith_Data.mk_sum;
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val long_mk_sum = Arith_Data.long_mk_sum;
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val dest_sum = Arith_Data.dest_sum;
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val mk_diff = HOLogic.mk_binop @{const_name Groups.minus};
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val dest_diff = HOLogic.dest_bin @{const_name Groups.minus} Term.dummyT;
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val mk_times = HOLogic.mk_binop @{const_name Groups.times};
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fun one_of T = Const(@{const_name Groups.one}, T);
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(* build product with trailing 1 rather than Numeral 1 in order to avoid the
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   unnecessary restriction to type class number_ring
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   which is not required for cancellation of common factors in divisions.
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*)
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fun mk_prod T = 
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  let val one = one_of T
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  fun mk [] = one
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    | mk [t] = t
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    | mk (t :: ts) = if t = one then mk ts else mk_times (t, mk ts)
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  in mk end;
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(*This version ALWAYS includes a trailing one*)
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fun long_mk_prod T []        = one_of T
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  | long_mk_prod T (t :: ts) = mk_times (t, mk_prod T ts);
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val dest_times = HOLogic.dest_bin @{const_name Groups.times} Term.dummyT;
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fun dest_prod t =
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      let val (t,u) = dest_times t
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      in dest_prod t @ dest_prod u end
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      handle TERM _ => [t];
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fun find_first_numeral past (t::terms) =
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        ((snd (HOLogic.dest_number t), rev past @ terms)
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         handle TERM _ => find_first_numeral (t::past) terms)
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  | find_first_numeral past [] = raise TERM("find_first_numeral", []);
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(*DON'T do the obvious simplifications; that would create special cases*)
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fun mk_coeff (k, t) = mk_times (mk_number (Term.fastype_of t) k, t);
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(*Express t as a product of (possibly) a numeral with other sorted terms*)
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fun dest_coeff sign (Const (@{const_name Groups.uminus}, _) $ t) = dest_coeff (~sign) t
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  | dest_coeff sign t =
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    let val ts = sort Term_Ord.term_ord (dest_prod t)
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        val (n, ts') = find_first_numeral [] ts
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                          handle TERM _ => (1, ts)
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    in (sign*n, mk_prod (Term.fastype_of t) ts') end;
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(*Find first coefficient-term THAT MATCHES u*)
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fun find_first_coeff past u [] = raise TERM("find_first_coeff", [])
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  | find_first_coeff past u (t::terms) =
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        let val (n,u') = dest_coeff 1 t
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        in if u aconv u' then (n, rev past @ terms)
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                         else find_first_coeff (t::past) u terms
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        end
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        handle TERM _ => find_first_coeff (t::past) u terms;
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(*Fractions as pairs of ints. Can't use Rat.rat because the representation
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  needs to preserve negative values in the denominator.*)
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fun mk_frac (p, q) = if q = 0 then raise Div else (p, q);
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(*Don't reduce fractions; sums must be proved by rule add_frac_eq.
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  Fractions are reduced later by the cancel_numeral_factor simproc.*)
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fun add_frac ((p1, q1), (p2, q2)) = (p1 * q2 + p2 * q1, q1 * q2);
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val mk_divide = HOLogic.mk_binop @{const_name Rings.divide};
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(*Build term (p / q) * t*)
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fun mk_fcoeff ((p, q), t) =
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  let val T = Term.fastype_of t
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  in mk_times (mk_divide (mk_number T p, mk_number T q), t) end;
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(*Express t as a product of a fraction with other sorted terms*)
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fun dest_fcoeff sign (Const (@{const_name Groups.uminus}, _) $ t) = dest_fcoeff (~sign) t
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  | dest_fcoeff sign (Const (@{const_name Rings.divide}, _) $ t $ u) =
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    let val (p, t') = dest_coeff sign t
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        val (q, u') = dest_coeff 1 u
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    in (mk_frac (p, q), mk_divide (t', u')) end
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  | dest_fcoeff sign t =
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    let val (p, t') = dest_coeff sign t
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        val T = Term.fastype_of t
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    in (mk_frac (p, 1), mk_divide (t', one_of T)) end;
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(** New term ordering so that AC-rewriting brings numerals to the front **)
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(*Order integers by absolute value and then by sign. The standard integer
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  ordering is not well-founded.*)
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fun num_ord (i,j) =
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  (case int_ord (abs i, abs j) of
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    EQUAL => int_ord (Int.sign i, Int.sign j) 
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  | ord => ord);
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(*This resembles Term_Ord.term_ord, but it puts binary numerals before other
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  non-atomic terms.*)
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local open Term 
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in 
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fun numterm_ord (Abs (_, T, t), Abs(_, U, u)) =
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      (case numterm_ord (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord)
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  | numterm_ord
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     (Const(@{const_name Int.number_of}, _) $ v, Const(@{const_name Int.number_of}, _) $ w) =
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     num_ord (HOLogic.dest_numeral v, HOLogic.dest_numeral w)
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  | numterm_ord (Const(@{const_name Int.number_of}, _) $ _, _) = LESS
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  | numterm_ord (_, Const(@{const_name Int.number_of}, _) $ _) = GREATER
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  | numterm_ord (t, u) =
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      (case int_ord (size_of_term t, size_of_term u) of
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        EQUAL =>
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          let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
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            (case Term_Ord.hd_ord (f, g) of EQUAL => numterms_ord (ts, us) | ord => ord)
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          end
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      | ord => ord)
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and numterms_ord (ts, us) = list_ord numterm_ord (ts, us)
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end;
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fun numtermless tu = (numterm_ord tu = LESS);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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val num_ss = HOL_ss settermless numtermless;
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(*Maps 0 to Numeral0 and 1 to Numeral1 so that arithmetic isn't complicated by the abstract 0 and 1.*)
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val numeral_syms = [@{thm numeral_0_eq_0} RS sym, @{thm numeral_1_eq_1} RS sym];
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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(*Simplify Numeral0+n, n+Numeral0, Numeral1*n, n*Numeral1, 1*x, x*1, x/1 *)
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val add_0s =  @{thms add_0s};
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val mult_1s = @{thms mult_1s mult_1_left mult_1_right divide_1};
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(*Simplify inverse Numeral1, a/Numeral1*)
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val inverse_1s = [@{thm inverse_numeral_1}];
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val divide_1s = [@{thm divide_numeral_1}];
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(*To perform binary arithmetic.  The "left" rewriting handles patterns
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  created by the Numeral_Simprocs, such as 3 * (5 * x). *)
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val simps = [@{thm numeral_0_eq_0} RS sym, @{thm numeral_1_eq_1} RS sym,
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                 @{thm add_number_of_left}, @{thm mult_number_of_left}] @
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                @{thms arith_simps} @ @{thms rel_simps};
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(*Binary arithmetic BUT NOT ADDITION since it may collapse adjacent terms
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  during re-arrangement*)
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val non_add_simps =
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  subtract Thm.eq_thm [@{thm add_number_of_left}, @{thm number_of_add} RS sym] simps;
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(*To evaluate binary negations of coefficients*)
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val minus_simps = [@{thm numeral_m1_eq_minus_1} RS sym, @{thm number_of_minus} RS sym] @
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                   @{thms minus_bin_simps} @ @{thms pred_bin_simps};
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(*To let us treat subtraction as addition*)
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val diff_simps = [@{thm diff_minus}, @{thm minus_add_distrib}, @{thm minus_minus}];
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(*To let us treat division as multiplication*)
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val divide_simps = [@{thm divide_inverse}, @{thm inverse_mult_distrib}, @{thm inverse_inverse_eq}];
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862a20ffa8e2 prefer explicit @{lemma} over adhoc forward reasoning;
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(*push the unary minus down*)
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val minus_mult_eq_1_to_2 = @{lemma "- (a::'a::ring) * b = a * - b" by simp};
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(*to extract again any uncancelled minuses*)
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val minus_from_mult_simps =
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    [@{thm minus_minus}, @{thm mult_minus_left}, @{thm mult_minus_right}];
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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(*combine unary minus with numeric literals, however nested within a product*)
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val mult_minus_simps =
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    [@{thm mult_assoc}, @{thm minus_mult_left}, minus_mult_eq_1_to_2];
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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val norm_ss1 = num_ss addsimps numeral_syms @ add_0s @ mult_1s @
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  diff_simps @ minus_simps @ @{thms add_ac}
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val norm_ss2 = num_ss addsimps non_add_simps @ mult_minus_simps
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val norm_ss3 = num_ss addsimps minus_from_mult_simps @ @{thms add_ac} @ @{thms mult_ac}
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structure CancelNumeralsCommon =
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  struct
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  val mk_sum            = mk_sum
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  val dest_sum          = dest_sum
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  val mk_coeff          = mk_coeff
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  val dest_coeff        = dest_coeff 1
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  val find_first_coeff  = find_first_coeff []
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  fun trans_tac _       = Arith_Data.trans_tac
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  fun norm_tac ss =
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    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1))
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val numeral_simp_ss = HOL_ss addsimps add_0s @ simps
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
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  val simplify_meta_eq = Arith_Data.simplify_meta_eq (add_0s @ mult_1s)
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  end;
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure EqCancelNumerals = CancelNumeralsFun
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 (open CancelNumeralsCommon
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val prove_conv = Arith_Data.prove_conv
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  val mk_bal   = HOLogic.mk_eq
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  val dest_bal = HOLogic.dest_bin "op =" Term.dummyT
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  val bal_add1 = @{thm eq_add_iff1} RS trans
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  val bal_add2 = @{thm eq_add_iff2} RS trans
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);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure LessCancelNumerals = CancelNumeralsFun
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 (open CancelNumeralsCommon
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  val prove_conv = Arith_Data.prove_conv
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cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
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  val mk_bal   = HOLogic.mk_binrel @{const_name Orderings.less}
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
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  val dest_bal = HOLogic.dest_bin @{const_name Orderings.less} Term.dummyT
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  val bal_add1 = @{thm less_add_iff1} RS trans
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  val bal_add2 = @{thm less_add_iff2} RS trans
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);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure LeCancelNumerals = CancelNumeralsFun
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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 (open CancelNumeralsCommon
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  val prove_conv = Arith_Data.prove_conv
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  val mk_bal   = HOLogic.mk_binrel @{const_name Orderings.less_eq}
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  val dest_bal = HOLogic.dest_bin @{const_name Orderings.less_eq} Term.dummyT
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  val bal_add1 = @{thm le_add_iff1} RS trans
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  val bal_add2 = @{thm le_add_iff2} RS trans
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   246
);
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   247
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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val cancel_numerals =
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  map (Arith_Data.prep_simproc @{theory})
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   [("inteq_cancel_numerals",
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     ["(l::'a::number_ring) + m = n",
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      "(l::'a::number_ring) = m + n",
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      "(l::'a::number_ring) - m = n",
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      "(l::'a::number_ring) = m - n",
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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      "(l::'a::number_ring) * m = n",
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      "(l::'a::number_ring) = m * n"],
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     K EqCancelNumerals.proc),
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   258
    ("intless_cancel_numerals",
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     ["(l::'a::{linordered_idom,number_ring}) + m < n",
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      "(l::'a::{linordered_idom,number_ring}) < m + n",
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      "(l::'a::{linordered_idom,number_ring}) - m < n",
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      "(l::'a::{linordered_idom,number_ring}) < m - n",
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      "(l::'a::{linordered_idom,number_ring}) * m < n",
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      "(l::'a::{linordered_idom,number_ring}) < m * n"],
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   265
     K LessCancelNumerals.proc),
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    ("intle_cancel_numerals",
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     ["(l::'a::{linordered_idom,number_ring}) + m <= n",
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      "(l::'a::{linordered_idom,number_ring}) <= m + n",
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      "(l::'a::{linordered_idom,number_ring}) - m <= n",
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      "(l::'a::{linordered_idom,number_ring}) <= m - n",
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      "(l::'a::{linordered_idom,number_ring}) * m <= n",
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      "(l::'a::{linordered_idom,number_ring}) <= m * n"],
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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     K LeCancelNumerals.proc)];
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   274
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure CombineNumeralsData =
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  struct
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  type coeff            = int
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  val iszero            = (fn x => x = 0)
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  val add               = op +
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val mk_sum            = long_mk_sum    (*to work for e.g. 2*x + 3*x *)
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  val dest_sum          = dest_sum
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  val mk_coeff          = mk_coeff
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  val dest_coeff        = dest_coeff 1
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  val left_distrib      = @{thm combine_common_factor} RS trans
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  val prove_conv        = Arith_Data.prove_conv_nohyps
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  fun trans_tac _       = Arith_Data.trans_tac
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  fun norm_tac ss =
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    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1))
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   293
  val numeral_simp_ss = HOL_ss addsimps add_0s @ simps
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  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
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  val simplify_meta_eq = Arith_Data.simplify_meta_eq (add_0s @ mult_1s)
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  end;
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData);
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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(*Version for fields, where coefficients can be fractions*)
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structure FieldCombineNumeralsData =
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  struct
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  type coeff            = int * int
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  val iszero            = (fn (p, q) => p = 0)
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  val add               = add_frac
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  val mk_sum            = long_mk_sum
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  val dest_sum          = dest_sum
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   308
  val mk_coeff          = mk_fcoeff
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  val dest_coeff        = dest_fcoeff 1
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   310
  val left_distrib      = @{thm combine_common_factor} RS trans
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   311
  val prove_conv        = Arith_Data.prove_conv_nohyps
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  fun trans_tac _       = Arith_Data.trans_tac
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   313
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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  val norm_ss1a = norm_ss1 addsimps inverse_1s @ divide_simps
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   315
  fun norm_tac ss =
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    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1a))
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   317
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
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   318
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
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   319
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   320
  val numeral_simp_ss = HOL_ss addsimps add_0s @ simps @ [@{thm add_frac_eq}]
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   321
  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
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   322
  val simplify_meta_eq = Arith_Data.simplify_meta_eq (add_0s @ mult_1s @ divide_1s)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   323
  end;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   324
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   325
structure FieldCombineNumerals = CombineNumeralsFun(FieldCombineNumeralsData);
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   326
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   327
val combine_numerals =
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  Arith_Data.prep_simproc @{theory}
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   329
    ("int_combine_numerals", 
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   330
     ["(i::'a::number_ring) + j", "(i::'a::number_ring) - j"], 
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   331
     K CombineNumerals.proc);
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   332
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   333
val field_combine_numerals =
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   334
  Arith_Data.prep_simproc @{theory}
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   335
    ("field_combine_numerals", 
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     ["(i::'a::{field_inverse_zero, number_ring}) + j",
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   337
      "(i::'a::{field_inverse_zero, number_ring}) - j"], 
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   338
     K FieldCombineNumerals.proc);
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   339
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   340
(** Constant folding for multiplication in semirings **)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   341
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   342
(*We do not need folding for addition: combine_numerals does the same thing*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   343
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   344
structure Semiring_Times_Assoc_Data : ASSOC_FOLD_DATA =
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   345
struct
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   346
  val assoc_ss = HOL_ss addsimps @{thms mult_ac}
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   347
  val eq_reflection = eq_reflection
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   348
  val is_numeral = can HOLogic.dest_number
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   349
end;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   350
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   351
structure Semiring_Times_Assoc = Assoc_Fold (Semiring_Times_Assoc_Data);
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   352
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   353
val assoc_fold_simproc =
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  Arith_Data.prep_simproc @{theory}
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f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   355
   ("semiring_assoc_fold", ["(a::'a::comm_semiring_1_cancel) * b"],
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
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   356
    K Semiring_Times_Assoc.proc);
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   357
69e55066dbca moved Integ files to canonical place;
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   358
structure CancelNumeralFactorCommon =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   359
  struct
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   360
  val mk_coeff          = mk_coeff
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   361
  val dest_coeff        = dest_coeff 1
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   362
  fun trans_tac _       = Arith_Data.trans_tac
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   363
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   364
  val norm_ss1 = HOL_ss addsimps minus_from_mult_simps @ mult_1s
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   365
  val norm_ss2 = HOL_ss addsimps simps @ mult_minus_simps
23881
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   366
  val norm_ss3 = HOL_ss addsimps @{thms mult_ac}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   367
  fun norm_tac ss =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   368
    ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss1))
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   369
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss2))
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   370
    THEN ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss3))
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   371
31068
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   372
  val numeral_simp_ss = HOL_ss addsimps
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   373
    [@{thm eq_number_of_eq}, @{thm less_number_of}, @{thm le_number_of}] @ simps
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   374
  fun numeral_simp_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss numeral_simp_ss))
30518
07b45c1aa788 moved some generic nonsense to arith_data.ML
haftmann
parents: 30496
diff changeset
   375
  val simplify_meta_eq = Arith_Data.simplify_meta_eq
35064
1bdef0c013d3 hide fact names clashing with fact names from Group.thy
haftmann
parents: 35050
diff changeset
   376
    [@{thm Nat.add_0}, @{thm Nat.add_0_right}, @{thm mult_zero_left},
26086
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 25481
diff changeset
   377
      @{thm mult_zero_right}, @{thm mult_Bit1}, @{thm mult_1_right}];
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   378
  end
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   379
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   380
(*Version for semiring_div*)
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   381
structure DivCancelNumeralFactor = CancelNumeralFactorFun
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   382
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   383
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   384
  val mk_bal   = HOLogic.mk_binop @{const_name Divides.div}
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   385
  val dest_bal = HOLogic.dest_bin @{const_name Divides.div} Term.dummyT
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   386
  val cancel = @{thm div_mult_mult1} RS trans
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   387
  val neg_exchanges = false
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   388
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   389
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   390
(*Version for fields*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   391
structure DivideCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   392
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   393
  val prove_conv = Arith_Data.prove_conv
35084
e25eedfc15ce moved constants inverse and divide to Ring.thy
haftmann
parents: 35064
diff changeset
   394
  val mk_bal   = HOLogic.mk_binop @{const_name Rings.divide}
e25eedfc15ce moved constants inverse and divide to Ring.thy
haftmann
parents: 35064
diff changeset
   395
  val dest_bal = HOLogic.dest_bin @{const_name Rings.divide} Term.dummyT
23413
5caa2710dd5b tuned laws for cancellation in divisions for fields.
nipkow
parents: 23401
diff changeset
   396
  val cancel = @{thm mult_divide_mult_cancel_left} RS trans
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   397
  val neg_exchanges = false
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   398
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   399
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   400
structure EqCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   401
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   402
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   403
  val mk_bal   = HOLogic.mk_eq
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   404
  val dest_bal = HOLogic.dest_bin "op =" Term.dummyT
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   405
  val cancel = @{thm mult_cancel_left} RS trans
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   406
  val neg_exchanges = false
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   407
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   408
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   409
structure LessCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   410
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   411
  val prove_conv = Arith_Data.prove_conv
35092
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   412
  val mk_bal   = HOLogic.mk_binrel @{const_name Orderings.less}
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   413
  val dest_bal = HOLogic.dest_bin @{const_name Orderings.less} Term.dummyT
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   414
  val cancel = @{thm mult_less_cancel_left} RS trans
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   415
  val neg_exchanges = true
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   416
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   417
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   418
structure LeCancelNumeralFactor = CancelNumeralFactorFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   419
 (open CancelNumeralFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   420
  val prove_conv = Arith_Data.prove_conv
35092
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   421
  val mk_bal   = HOLogic.mk_binrel @{const_name Orderings.less_eq}
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   422
  val dest_bal = HOLogic.dest_bin @{const_name Orderings.less_eq} Term.dummyT
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   423
  val cancel = @{thm mult_le_cancel_left} RS trans
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   424
  val neg_exchanges = true
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   425
)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   426
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   427
val cancel_numeral_factors =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   428
  map (Arith_Data.prep_simproc @{theory})
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   429
   [("ring_eq_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   430
     ["(l::'a::{idom,number_ring}) * m = n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   431
      "(l::'a::{idom,number_ring}) = m * n"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   432
     K EqCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   433
    ("ring_less_cancel_numeral_factor",
35028
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   434
     ["(l::'a::{linordered_idom,number_ring}) * m < n",
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   435
      "(l::'a::{linordered_idom,number_ring}) < m * n"],
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   436
     K LessCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   437
    ("ring_le_cancel_numeral_factor",
35028
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   438
     ["(l::'a::{linordered_idom,number_ring}) * m <= n",
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   439
      "(l::'a::{linordered_idom,number_ring}) <= m * n"],
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   440
     K LeCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   441
    ("int_div_cancel_numeral_factors",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   442
     ["((l::'a::{semiring_div,number_ring}) * m) div n",
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   443
      "(l::'a::{semiring_div,number_ring}) div (m * n)"],
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   444
     K DivCancelNumeralFactor.proc),
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   445
    ("divide_cancel_numeral_factor",
36409
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   446
     ["((l::'a::{field_inverse_zero,number_ring}) * m) / n",
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   447
      "(l::'a::{field_inverse_zero,number_ring}) / (m * n)",
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   448
      "((number_of v)::'a::{field_inverse_zero,number_ring}) / (number_of w)"],
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   449
     K DivideCancelNumeralFactor.proc)];
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   450
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   451
val field_cancel_numeral_factors =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   452
  map (Arith_Data.prep_simproc @{theory})
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   453
   [("field_eq_cancel_numeral_factor",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   454
     ["(l::'a::{field,number_ring}) * m = n",
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   455
      "(l::'a::{field,number_ring}) = m * n"],
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   456
     K EqCancelNumeralFactor.proc),
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   457
    ("field_cancel_numeral_factor",
36409
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   458
     ["((l::'a::{field_inverse_zero,number_ring}) * m) / n",
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   459
      "(l::'a::{field_inverse_zero,number_ring}) / (m * n)",
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   460
      "((number_of v)::'a::{field_inverse_zero,number_ring}) / (number_of w)"],
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   461
     K DivideCancelNumeralFactor.proc)]
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   462
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   463
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   464
(** Declarations for ExtractCommonTerm **)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   465
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   466
(*Find first term that matches u*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   467
fun find_first_t past u []         = raise TERM ("find_first_t", [])
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   468
  | find_first_t past u (t::terms) =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   469
        if u aconv t then (rev past @ terms)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   470
        else find_first_t (t::past) u terms
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   471
        handle TERM _ => find_first_t (t::past) u terms;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   472
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   473
(** Final simplification for the CancelFactor simprocs **)
30518
07b45c1aa788 moved some generic nonsense to arith_data.ML
haftmann
parents: 30496
diff changeset
   474
val simplify_one = Arith_Data.simplify_meta_eq  
30031
bd786c37af84 Removed redundant lemmas
nipkow
parents: 29981
diff changeset
   475
  [@{thm mult_1_left}, @{thm mult_1_right}, @{thm div_by_1}, @{thm numeral_1_eq_1}];
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   476
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   477
fun cancel_simplify_meta_eq ss cancel_th th =
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   478
    simplify_one ss (([th, cancel_th]) MRS trans);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   479
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   480
local
31067
fd7ec31f850c generalized simproc for mod
haftmann
parents: 30931
diff changeset
   481
  val Tp_Eq = Thm.reflexive (Thm.cterm_of @{theory HOL} HOLogic.Trueprop)
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   482
  fun Eq_True_elim Eq = 
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   483
    Thm.equal_elim (Thm.combination Tp_Eq (Thm.symmetric Eq)) @{thm TrueI}
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   484
in
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   485
fun sign_conv pos_th neg_th ss t =
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   486
  let val T = fastype_of t;
35267
8dfd816713c6 moved remaning class operations from Algebras.thy to Groups.thy
haftmann
parents: 35092
diff changeset
   487
      val zero = Const(@{const_name Groups.zero}, T);
35092
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   488
      val less = Const(@{const_name Orderings.less}, [T,T] ---> HOLogic.boolT);
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   489
      val pos = less $ zero $ t and neg = less $ t $ zero
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   490
      fun prove p =
31101
26c7bb764a38 qualified names for Lin_Arith tactics and simprocs
haftmann
parents: 31068
diff changeset
   491
        Option.map Eq_True_elim (Lin_Arith.simproc ss p)
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   492
        handle THM _ => NONE
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   493
    in case prove pos of
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   494
         SOME th => SOME(th RS pos_th)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   495
       | NONE => (case prove neg of
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   496
                    SOME th => SOME(th RS neg_th)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   497
                  | NONE => NONE)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   498
    end;
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   499
end
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   500
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   501
structure CancelFactorCommon =
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   502
  struct
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   503
  val mk_sum            = long_mk_prod
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   504
  val dest_sum          = dest_prod
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   505
  val mk_coeff          = mk_coeff
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   506
  val dest_coeff        = dest_coeff
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   507
  val find_first        = find_first_t []
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   508
  fun trans_tac _       = Arith_Data.trans_tac
23881
851c74f1bb69 moved class ord from Orderings.thy to HOL.thy
haftmann
parents: 23413
diff changeset
   509
  val norm_ss = HOL_ss addsimps mult_1s @ @{thms mult_ac}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   510
  fun norm_tac ss = ALLGOALS (simp_tac (Simplifier.inherit_context ss norm_ss))
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   511
  val simplify_meta_eq  = cancel_simplify_meta_eq 
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   512
  end;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   513
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   514
(*mult_cancel_left requires a ring with no zero divisors.*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   515
structure EqCancelFactor = ExtractCommonTermFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   516
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   517
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   518
  val mk_bal   = HOLogic.mk_eq
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   519
  val dest_bal = HOLogic.dest_bin "op =" Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   520
  fun simp_conv _ _ = SOME @{thm mult_cancel_left}
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   521
);
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   522
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   523
(*for ordered rings*)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   524
structure LeCancelFactor = ExtractCommonTermFun
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   525
 (open CancelFactorCommon
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   526
  val prove_conv = Arith_Data.prove_conv
35092
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   527
  val mk_bal   = HOLogic.mk_binrel @{const_name Orderings.less_eq}
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   528
  val dest_bal = HOLogic.dest_bin @{const_name Orderings.less_eq} Term.dummyT
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   529
  val simp_conv = sign_conv
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   530
    @{thm mult_le_cancel_left_pos} @{thm mult_le_cancel_left_neg}
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   531
);
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   532
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   533
(*for ordered rings*)
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   534
structure LessCancelFactor = ExtractCommonTermFun
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   535
 (open CancelFactorCommon
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   536
  val prove_conv = Arith_Data.prove_conv
35092
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   537
  val mk_bal   = HOLogic.mk_binrel @{const_name Orderings.less}
cfe605c54e50 moved less_eq, less to Orderings.thy; moved abs, sgn to Groups.thy
haftmann
parents: 35084
diff changeset
   538
  val dest_bal = HOLogic.dest_bin @{const_name Orderings.less} Term.dummyT
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   539
  val simp_conv = sign_conv
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   540
    @{thm mult_less_cancel_left_pos} @{thm mult_less_cancel_left_neg}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   541
);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   542
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   543
(*for semirings with division*)
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   544
structure DivCancelFactor = ExtractCommonTermFun
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   545
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   546
  val prove_conv = Arith_Data.prove_conv
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   547
  val mk_bal   = HOLogic.mk_binop @{const_name Divides.div}
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   548
  val dest_bal = HOLogic.dest_bin @{const_name Divides.div} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   549
  fun simp_conv _ _ = SOME @{thm div_mult_mult1_if}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   550
);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   551
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   552
structure ModCancelFactor = ExtractCommonTermFun
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   553
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   554
  val prove_conv = Arith_Data.prove_conv
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   555
  val mk_bal   = HOLogic.mk_binop @{const_name Divides.mod}
31067
fd7ec31f850c generalized simproc for mod
haftmann
parents: 30931
diff changeset
   556
  val dest_bal = HOLogic.dest_bin @{const_name Divides.mod} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   557
  fun simp_conv _ _ = SOME @{thm mod_mult_mult1}
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   558
);
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   559
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   560
(*for idoms*)
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   561
structure DvdCancelFactor = ExtractCommonTermFun
23969
ef782bbf2d09 Added cancel simprocs for dvd on nat and int
nipkow
parents: 23881
diff changeset
   562
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   563
  val prove_conv = Arith_Data.prove_conv
35050
9f841f20dca6 renamed OrderedGroup to Groups; split theory Ring_and_Field into Rings Fields
haftmann
parents: 35043
diff changeset
   564
  val mk_bal   = HOLogic.mk_binrel @{const_name Rings.dvd}
9f841f20dca6 renamed OrderedGroup to Groups; split theory Ring_and_Field into Rings Fields
haftmann
parents: 35043
diff changeset
   565
  val dest_bal = HOLogic.dest_bin @{const_name Rings.dvd} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   566
  fun simp_conv _ _ = SOME @{thm dvd_mult_cancel_left}
23969
ef782bbf2d09 Added cancel simprocs for dvd on nat and int
nipkow
parents: 23881
diff changeset
   567
);
ef782bbf2d09 Added cancel simprocs for dvd on nat and int
nipkow
parents: 23881
diff changeset
   568
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   569
(*Version for all fields, including unordered ones (type complex).*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   570
structure DivideCancelFactor = ExtractCommonTermFun
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   571
 (open CancelFactorCommon
30496
7cdcc9dd95cb vague cleanup in arith proof tools setup: deleted dead code, more proper structures, clearer arrangement
haftmann
parents: 30242
diff changeset
   572
  val prove_conv = Arith_Data.prove_conv
35084
e25eedfc15ce moved constants inverse and divide to Ring.thy
haftmann
parents: 35064
diff changeset
   573
  val mk_bal   = HOLogic.mk_binop @{const_name Rings.divide}
e25eedfc15ce moved constants inverse and divide to Ring.thy
haftmann
parents: 35064
diff changeset
   574
  val dest_bal = HOLogic.dest_bin @{const_name Rings.divide} Term.dummyT
31368
763f4b0fd579 made SML/NJ happy;
wenzelm
parents: 31101
diff changeset
   575
  fun simp_conv _ _ = SOME @{thm mult_divide_mult_cancel_left_if}
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   576
);
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   577
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   578
val cancel_factors =
32155
e2bf2f73b0c8 more @{theory} antiquotations;
wenzelm
parents: 31368
diff changeset
   579
  map (Arith_Data.prep_simproc @{theory})
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   580
   [("ring_eq_cancel_factor",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   581
     ["(l::'a::idom) * m = n",
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   582
      "(l::'a::idom) = m * n"],
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   583
     K EqCancelFactor.proc),
35043
07dbdf60d5ad dropped accidental duplication of "lin" prefix from cs. 108662d50512
haftmann
parents: 35030
diff changeset
   584
    ("linordered_ring_le_cancel_factor",
35028
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   585
     ["(l::'a::linordered_ring) * m <= n",
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   586
      "(l::'a::linordered_ring) <= m * n"],
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   587
     K LeCancelFactor.proc),
35043
07dbdf60d5ad dropped accidental duplication of "lin" prefix from cs. 108662d50512
haftmann
parents: 35030
diff changeset
   588
    ("linordered_ring_less_cancel_factor",
35028
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   589
     ["(l::'a::linordered_ring) * m < n",
108662d50512 more consistent naming of type classes involving orderings (and lattices) -- c.f. NEWS
haftmann
parents: 34974
diff changeset
   590
      "(l::'a::linordered_ring) < m * n"],
30649
57753e0ec1d4 1. New cancellation simprocs for common factors in inequations
nipkow
parents: 30518
diff changeset
   591
     K LessCancelFactor.proc),
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   592
    ("int_div_cancel_factor",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   593
     ["((l::'a::semiring_div) * m) div n", "(l::'a::semiring_div) div (m * n)"],
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   594
     K DivCancelFactor.proc),
24395
8df021f79e0b Added mod cancellation simproc
nipkow
parents: 23969
diff changeset
   595
    ("int_mod_cancel_factor",
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   596
     ["((l::'a::semiring_div) * m) mod n", "(l::'a::semiring_div) mod (m * n)"],
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   597
     K ModCancelFactor.proc),
29981
7d0ed261b712 generalize int_dvd_cancel_factor simproc to idom class
huffman
parents: 29038
diff changeset
   598
    ("dvd_cancel_factor",
7d0ed261b712 generalize int_dvd_cancel_factor simproc to idom class
huffman
parents: 29038
diff changeset
   599
     ["((l::'a::idom) * m) dvd n", "(l::'a::idom) dvd (m * n)"],
30931
86ca651da03e generalized some simprocs from int to semiring_div
haftmann
parents: 30685
diff changeset
   600
     K DvdCancelFactor.proc),
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   601
    ("divide_cancel_factor",
36409
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   602
     ["((l::'a::field_inverse_zero) * m) / n",
d323e7773aa8 use new classes (linordered_)field_inverse_zero
haftmann
parents: 36349
diff changeset
   603
      "(l::'a::field_inverse_zero) / (m * n)"],
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   604
     K DivideCancelFactor.proc)];
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   605
36751
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   606
local
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   607
 val zr = @{cpat "0"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   608
 val zT = ctyp_of_term zr
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   609
 val geq = @{cpat "op ="}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   610
 val eqT = Thm.dest_ctyp (ctyp_of_term geq) |> hd
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   611
 val add_frac_eq = mk_meta_eq @{thm "add_frac_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   612
 val add_frac_num = mk_meta_eq @{thm "add_frac_num"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   613
 val add_num_frac = mk_meta_eq @{thm "add_num_frac"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   614
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   615
 fun prove_nz ss T t =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   616
    let
36945
9bec62c10714 less pervasive names from structure Thm;
wenzelm
parents: 36751
diff changeset
   617
      val z = Thm.instantiate_cterm ([(zT,T)],[]) zr
9bec62c10714 less pervasive names from structure Thm;
wenzelm
parents: 36751
diff changeset
   618
      val eq = Thm.instantiate_cterm ([(eqT,T)],[]) geq
36751
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   619
      val th = Simplifier.rewrite (ss addsimps @{thms simp_thms})
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   620
           (Thm.capply @{cterm "Trueprop"} (Thm.capply @{cterm "Not"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   621
                  (Thm.capply (Thm.capply eq t) z)))
36945
9bec62c10714 less pervasive names from structure Thm;
wenzelm
parents: 36751
diff changeset
   622
    in Thm.equal_elim (Thm.symmetric th) TrueI
36751
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   623
    end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   624
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   625
 fun proc phi ss ct =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   626
  let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   627
    val ((x,y),(w,z)) =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   628
         (Thm.dest_binop #> (fn (a,b) => (Thm.dest_binop a, Thm.dest_binop b))) ct
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   629
    val _ = map (HOLogic.dest_number o term_of) [x,y,z,w]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   630
    val T = ctyp_of_term x
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   631
    val [y_nz, z_nz] = map (prove_nz ss T) [y, z]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   632
    val th = instantiate' [SOME T] (map SOME [y,z,x,w]) add_frac_eq
36945
9bec62c10714 less pervasive names from structure Thm;
wenzelm
parents: 36751
diff changeset
   633
  in SOME (Thm.implies_elim (Thm.implies_elim th y_nz) z_nz)
36751
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   634
  end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   635
  handle CTERM _ => NONE | TERM _ => NONE | THM _ => NONE
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   636
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   637
 fun proc2 phi ss ct =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   638
  let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   639
    val (l,r) = Thm.dest_binop ct
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   640
    val T = ctyp_of_term l
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   641
  in (case (term_of l, term_of r) of
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   642
      (Const(@{const_name Rings.divide},_)$_$_, _) =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   643
        let val (x,y) = Thm.dest_binop l val z = r
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   644
            val _ = map (HOLogic.dest_number o term_of) [x,y,z]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   645
            val ynz = prove_nz ss T y
36945
9bec62c10714 less pervasive names from structure Thm;
wenzelm
parents: 36751
diff changeset
   646
        in SOME (Thm.implies_elim (instantiate' [SOME T] (map SOME [y,x,z]) add_frac_num) ynz)
36751
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   647
        end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   648
     | (_, Const (@{const_name Rings.divide},_)$_$_) =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   649
        let val (x,y) = Thm.dest_binop r val z = l
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   650
            val _ = map (HOLogic.dest_number o term_of) [x,y,z]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   651
            val ynz = prove_nz ss T y
36945
9bec62c10714 less pervasive names from structure Thm;
wenzelm
parents: 36751
diff changeset
   652
        in SOME (Thm.implies_elim (instantiate' [SOME T] (map SOME [y,z,x]) add_num_frac) ynz)
36751
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   653
        end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   654
     | _ => NONE)
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   655
  end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   656
  handle CTERM _ => NONE | TERM _ => NONE | THM _ => NONE
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   657
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   658
 fun is_number (Const(@{const_name Rings.divide},_)$a$b) = is_number a andalso is_number b
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   659
   | is_number t = can HOLogic.dest_number t
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   660
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   661
 val is_number = is_number o term_of
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   662
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   663
 fun proc3 phi ss ct =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   664
  (case term_of ct of
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   665
    Const(@{const_name Orderings.less},_)$(Const(@{const_name Rings.divide},_)$_$_)$_ =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   666
      let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   667
        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   668
        val _ = map is_number [a,b,c]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   669
        val T = ctyp_of_term c
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   670
        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_less_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   671
      in SOME (mk_meta_eq th) end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   672
  | Const(@{const_name Orderings.less_eq},_)$(Const(@{const_name Rings.divide},_)$_$_)$_ =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   673
      let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   674
        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   675
        val _ = map is_number [a,b,c]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   676
        val T = ctyp_of_term c
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   677
        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_le_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   678
      in SOME (mk_meta_eq th) end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   679
  | Const("op =",_)$(Const(@{const_name Rings.divide},_)$_$_)$_ =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   680
      let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   681
        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   682
        val _ = map is_number [a,b,c]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   683
        val T = ctyp_of_term c
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   684
        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_eq_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   685
      in SOME (mk_meta_eq th) end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   686
  | Const(@{const_name Orderings.less},_)$_$(Const(@{const_name Rings.divide},_)$_$_) =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   687
    let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   688
      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   689
        val _ = map is_number [a,b,c]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   690
        val T = ctyp_of_term c
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   691
        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "less_divide_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   692
      in SOME (mk_meta_eq th) end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   693
  | Const(@{const_name Orderings.less_eq},_)$_$(Const(@{const_name Rings.divide},_)$_$_) =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   694
    let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   695
      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   696
        val _ = map is_number [a,b,c]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   697
        val T = ctyp_of_term c
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   698
        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "le_divide_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   699
      in SOME (mk_meta_eq th) end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   700
  | Const("op =",_)$_$(Const(@{const_name Rings.divide},_)$_$_) =>
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   701
    let
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   702
      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   703
        val _ = map is_number [a,b,c]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   704
        val T = ctyp_of_term c
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   705
        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "eq_divide_eq"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   706
      in SOME (mk_meta_eq th) end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   707
  | _ => NONE)
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   708
  handle TERM _ => NONE | CTERM _ => NONE | THM _ => NONE
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   709
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   710
val add_frac_frac_simproc =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   711
       make_simproc {lhss = [@{cpat "(?x::?'a::field)/?y + (?w::?'a::field)/?z"}],
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   712
                     name = "add_frac_frac_simproc",
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   713
                     proc = proc, identifier = []}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   714
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   715
val add_frac_num_simproc =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   716
       make_simproc {lhss = [@{cpat "(?x::?'a::field)/?y + ?z"}, @{cpat "?z + (?x::?'a::field)/?y"}],
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   717
                     name = "add_frac_num_simproc",
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   718
                     proc = proc2, identifier = []}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   719
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   720
val ord_frac_simproc =
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   721
  make_simproc
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   722
    {lhss = [@{cpat "(?a::(?'a::{field, ord}))/?b < ?c"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   723
             @{cpat "(?a::(?'a::{field, ord}))/?b <= ?c"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   724
             @{cpat "?c < (?a::(?'a::{field, ord}))/?b"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   725
             @{cpat "?c <= (?a::(?'a::{field, ord}))/?b"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   726
             @{cpat "?c = ((?a::(?'a::{field, ord}))/?b)"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   727
             @{cpat "((?a::(?'a::{field, ord}))/ ?b) = ?c"}],
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   728
             name = "ord_frac_simproc", proc = proc3, identifier = []}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   729
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   730
val ths = [@{thm "mult_numeral_1"}, @{thm "mult_numeral_1_right"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   731
           @{thm "divide_Numeral1"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   732
           @{thm "divide_zero"}, @{thm "divide_Numeral0"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   733
           @{thm "divide_divide_eq_left"}, 
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   734
           @{thm "times_divide_eq_left"}, @{thm "times_divide_eq_right"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   735
           @{thm "times_divide_times_eq"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   736
           @{thm "divide_divide_eq_right"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   737
           @{thm "diff_def"}, @{thm "minus_divide_left"},
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   738
           @{thm "Numeral1_eq1_nat"}, @{thm "add_divide_distrib"} RS sym,
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   739
           @{thm field_divide_inverse} RS sym, @{thm inverse_divide}, 
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   740
           Conv.fconv_rule (Conv.arg_conv (Conv.arg1_conv (Conv.rewr_conv (mk_meta_eq @{thm mult_commute}))))   
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   741
           (@{thm field_divide_inverse} RS sym)]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   742
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   743
in
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   744
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   745
val field_comp_conv = (Simplifier.rewrite
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   746
(HOL_basic_ss addsimps @{thms "semiring_norm"}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   747
              addsimps ths addsimps @{thms simp_thms}
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   748
              addsimprocs field_cancel_numeral_factors
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   749
               addsimprocs [add_frac_frac_simproc, add_frac_num_simproc,
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   750
                            ord_frac_simproc]
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   751
                addcongs [@{thm "if_weak_cong"}]))
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   752
then_conv (Simplifier.rewrite (HOL_basic_ss addsimps
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   753
  [@{thm numeral_1_eq_1},@{thm numeral_0_eq_0}] @ @{thms numerals(1-2)}))
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   754
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   755
end
7f1da69cacb3 split of semiring normalization from Groebner theory; moved field_comp_conv to Numeral_Simproces
haftmann
parents: 36409
diff changeset
   756
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   757
end;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   758
31068
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   759
Addsimprocs Numeral_Simprocs.cancel_numerals;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   760
Addsimprocs [Numeral_Simprocs.combine_numerals];
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   761
Addsimprocs [Numeral_Simprocs.field_combine_numerals];
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   762
Addsimprocs [Numeral_Simprocs.assoc_fold_simproc];
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   763
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   764
(*examples:
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   765
print_depth 22;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   766
set timing;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   767
set trace_simp;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   768
fun test s = (Goal s, by (Simp_tac 1));
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   769
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   770
test "l + 2 + 2 + 2 + (l + 2) + (oo + 2) = (uu::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   771
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   772
test "2*u = (u::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   773
test "(i + j + 12 + (k::int)) - 15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   774
test "(i + j + 12 + (k::int)) - 5 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   775
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   776
test "y - b < (b::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   777
test "y - (3*b + c) < (b::int) - 2*c";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   778
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   779
test "(2*x - (u*v) + y) - v*3*u = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   780
test "(2*x*u*v + (u*v)*4 + y) - v*u*4 = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   781
test "(2*x*u*v + (u*v)*4 + y) - v*u = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   782
test "u*v - (x*u*v + (u*v)*4 + y) = (w::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   783
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   784
test "(i + j + 12 + (k::int)) = u + 15 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   785
test "(i + j*2 + 12 + (k::int)) = j + 5 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   786
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   787
test "2*y + 3*z + 6*w + 2*y + 3*z + 2*u = 2*y' + 3*z' + 6*w' + 2*y' + 3*z' + u + (vv::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   788
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   789
test "a + -(b+c) + b = (d::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   790
test "a + -(b+c) - b = (d::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   791
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   792
(*negative numerals*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   793
test "(i + j + -2 + (k::int)) - (u + 5 + y) = zz";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   794
test "(i + j + -3 + (k::int)) < u + 5 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   795
test "(i + j + 3 + (k::int)) < u + -6 + y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   796
test "(i + j + -12 + (k::int)) - 15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   797
test "(i + j + 12 + (k::int)) - -15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   798
test "(i + j + -12 + (k::int)) - -15 = y";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   799
*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   800
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   801
Addsimprocs Numeral_Simprocs.cancel_numeral_factors;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   802
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   803
(*examples:
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   804
print_depth 22;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   805
set timing;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   806
set trace_simp;
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   807
fun test s = (Goal s; by (Simp_tac 1));
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   808
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   809
test "9*x = 12 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   810
test "(9*x) div (12 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   811
test "9*x < 12 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   812
test "9*x <= 12 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   813
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   814
test "-99*x = 132 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   815
test "(-99*x) div (132 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   816
test "-99*x < 132 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   817
test "-99*x <= 132 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   818
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   819
test "999*x = -396 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   820
test "(999*x) div (-396 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   821
test "999*x < -396 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   822
test "999*x <= -396 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   823
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   824
test "-99*x = -81 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   825
test "(-99*x) div (-81 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   826
test "-99*x <= -81 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   827
test "-99*x < -81 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   828
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   829
test "-2 * x = -1 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   830
test "-2 * x = -(y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   831
test "(-2 * x) div (-1 * (y::int)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   832
test "-2 * x < -(y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   833
test "-2 * x <= -1 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   834
test "-x < -23 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   835
test "-x <= -23 * (y::int)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   836
*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   837
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   838
(*And the same examples for fields such as rat or real:
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   839
test "0 <= (y::rat) * -2";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   840
test "9*x = 12 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   841
test "(9*x) / (12 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   842
test "9*x < 12 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   843
test "9*x <= 12 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   844
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   845
test "-99*x = 132 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   846
test "(-99*x) / (132 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   847
test "-99*x < 132 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   848
test "-99*x <= 132 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   849
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   850
test "999*x = -396 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   851
test "(999*x) / (-396 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   852
test "999*x < -396 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   853
test "999*x <= -396 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   854
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   855
test  "(- ((2::rat) * x) <= 2 * y)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   856
test "-99*x = -81 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   857
test "(-99*x) / (-81 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   858
test "-99*x <= -81 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   859
test "-99*x < -81 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   860
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   861
test "-2 * x = -1 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   862
test "-2 * x = -(y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   863
test "(-2 * x) / (-1 * (y::rat)) = z";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   864
test "-2 * x < -(y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   865
test "-2 * x <= -1 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   866
test "-x < -23 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   867
test "-x <= -23 * (y::rat)";
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   868
*)
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   869
f591144b0f17 modules numeral_simprocs, nat_numeral_simprocs; proper structures for numeral simprocs
haftmann
parents: 31067
diff changeset
   870
Addsimprocs Numeral_Simprocs.cancel_factors;
23164
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   871
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   872
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   873
(*examples:
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   874
print_depth 22;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   875
set timing;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   876
set trace_simp;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   877
fun test s = (Goal s; by (Asm_simp_tac 1));
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   878
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   879
test "x*k = k*(y::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   880
test "k = k*(y::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   881
test "a*(b*c) = (b::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   882
test "a*(b*c) = d*(b::int)*(x*a)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   883
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   884
test "(x*k) div (k*(y::int)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   885
test "(k) div (k*(y::int)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   886
test "(a*(b*c)) div ((b::int)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   887
test "(a*(b*c)) div (d*(b::int)*(x*a)) = (uu::int)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   888
*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   889
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   890
(*And the same examples for fields such as rat or real:
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   891
print_depth 22;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   892
set timing;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   893
set trace_simp;
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   894
fun test s = (Goal s; by (Asm_simp_tac 1));
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   895
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   896
test "x*k = k*(y::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   897
test "k = k*(y::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   898
test "a*(b*c) = (b::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   899
test "a*(b*c) = d*(b::rat)*(x*a)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   900
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   901
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   902
test "(x*k) / (k*(y::rat)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   903
test "(k) / (k*(y::rat)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   904
test "(a*(b*c)) / ((b::rat)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   905
test "(a*(b*c)) / (d*(b::rat)*(x*a)) = (uu::rat)";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   906
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   907
(*FIXME: what do we do about this?*)
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   908
test "a*(b*c)/(y*z) = d*(b::rat)*(x*a)/z";
69e55066dbca moved Integ files to canonical place;
wenzelm
parents:
diff changeset
   909
*)