diff -r 3a8d722fd3ff -r 16c4ea954511 Subst/Subst.ML --- a/Subst/Subst.ML Fri Nov 11 10:35:03 1994 +0100 +++ b/Subst/Subst.ML Mon Nov 21 17:50:34 1994 +0100 @@ -34,12 +34,12 @@ goal Subst.thy "t <| Nil = t"; by (uterm_ind_tac "t" 1); by (ALLGOALS (asm_simp_tac (subst_ss addsimps [Var_subst]))); -val subst_Nil = result(); +qed "subst_Nil"; goal Subst.thy "t <: u --> t <| s <: u <| s"; by (uterm_ind_tac "u" 1); by (ALLGOALS (asm_simp_tac subst_ss)); -val subst_mono = result() RS mp; +val subst_mono = store_thm("subst_mono", result() RS mp); goal Subst.thy "~ (Var(v) <: t) --> t <| #s = t <| s"; by (imp_excluded_middle_tac "t = Var(v)" 1); @@ -48,7 +48,7 @@ uterm_induct 2); by (ALLGOALS (simp_tac (subst_ss addsimps [Var_subst]))); by (fast_tac HOL_cs 1); -val Var_not_occs = result() RS mp; +val Var_not_occs = store_thm("Var_not_occs", result() RS mp); goal Subst.thy "(t <|r = t <|s) = (! v.v : vars_of(t) --> Var(v) <|r = Var(v) <|s)"; @@ -56,24 +56,24 @@ by (REPEAT (etac rev_mp 3)); by (ALLGOALS (asm_simp_tac subst_ss)); by (ALLGOALS (fast_tac HOL_cs)); -val agreement = result(); +qed "agreement"; goal Subst.thy "~ v: vars_of(t) --> t <| #s = t <| s"; by(simp_tac(subst_ss addsimps [agreement,Var_subst] setloop (split_tac [expand_if])) 1); -val repl_invariance = result() RS mp; +val repl_invariance = store_thm("repl_invariance", result() RS mp); val asms = goal Subst.thy "v : vars_of(t) --> w : vars_of(t <| #s)"; by (uterm_ind_tac "t" 1); by (ALLGOALS (asm_simp_tac (subst_ss addsimps [Var_subst]))); -val Var_in_subst = result() RS mp; +val Var_in_subst = store_thm("Var_in_subst", result() RS mp); (**** Equality between Substitutions ****) goalw Subst.thy [subst_eq_def] "r =s= s = (! t.t <| r = t <| s)"; by (simp_tac subst_ss 1); -val subst_eq_iff = result(); +qed "subst_eq_iff"; local fun mk_thm s = prove_goal Subst.thy s (fn prems => [cut_facts_tac prems 1, @@ -89,7 +89,7 @@ "[| r =s= s; P(t <| r,u <| r) |] ==> P(t <| s,u <| s)"; by (resolve_tac [eq RS spec RS subst] 1); by (resolve_tac (prems RL [eq RS spec RS subst]) 1); -val subst_subst2 = result(); +qed "subst_subst2"; val ssubst_subst2 = subst_sym RS subst_subst2; @@ -98,7 +98,7 @@ goal Subst.thy "s <> Nil = s"; by (alist_ind_tac "s" 1); by (ALLGOALS (asm_simp_tac (subst_ss addsimps [subst_Nil]))); -val comp_Nil = result(); +qed "comp_Nil"; goal Subst.thy "(t <| r <> s) = (t <| r <| s)"; by (uterm_ind_tac "t" 1); @@ -106,11 +106,11 @@ by (alist_ind_tac "r" 1); by (ALLGOALS (asm_simp_tac (subst_ss addsimps [Var_subst,subst_Nil] setloop (split_tac [expand_if])))); -val subst_comp = result(); +qed "subst_comp"; goal Subst.thy "q <> r <> s =s= q <> (r <> s)"; by (simp_tac (subst_ss addsimps [subst_eq_iff,subst_comp]) 1); -val comp_assoc = result(); +qed "comp_assoc"; goal Subst.thy "#s =s= s"; by (rtac (allI RS (subst_eq_iff RS iffD2)) 1); @@ -118,12 +118,12 @@ by (REPEAT (etac rev_mp 3)); by (ALLGOALS (simp_tac (subst_ss addsimps[Var_subst] setloop (split_tac [expand_if])))); -val Cons_trivial = result(); +qed "Cons_trivial"; val [prem] = goal Subst.thy "q <> r =s= s ==> t <| q <| r = t <| s"; by (simp_tac (subst_ss addsimps [prem RS (subst_eq_iff RS iffD1), subst_comp RS sym]) 1); -val comp_subst_subst = result(); +qed "comp_subst_subst"; (**** Domain and range of Substitutions ****) @@ -132,31 +132,31 @@ by (ALLGOALS (asm_simp_tac (subst_ss addsimps [Var_subst] setloop (split_tac[expand_if])))); by (fast_tac HOL_cs 1); -val sdom_iff = result(); +qed "sdom_iff"; goalw Subst.thy [srange_def] "v : srange(s) = (? w.w : sdom(s) & v : vars_of(Var(w) <| s))"; by (fast_tac set_cs 1); -val srange_iff = result(); +qed "srange_iff"; goal Subst.thy "(t <| s = t) = (sdom(s) Int vars_of(t) = {})"; by (uterm_ind_tac "t" 1); by (REPEAT (etac rev_mp 3)); by (ALLGOALS (simp_tac (subst_ss addsimps [sdom_iff,Var_subst]))); by (ALLGOALS (fast_tac set_cs)); -val invariance = result(); +qed "invariance"; goal Subst.thy "v : sdom(s) --> ~v : srange(s) --> ~v : vars_of(t <| s)"; by (uterm_ind_tac "t" 1); by (imp_excluded_middle_tac "x : sdom(s)" 1); by (ALLGOALS (asm_simp_tac (subst_ss addsimps [sdom_iff,srange_iff]))); by (ALLGOALS (fast_tac set_cs)); -val Var_elim = result() RS mp RS mp; +val Var_elim = store_thm("Var_elim", result() RS mp RS mp); val asms = goal Subst.thy "[| v : sdom(s); v : vars_of(t <| s) |] ==> v : srange(s)"; by (REPEAT (ares_tac (asms @ [Var_elim RS swap RS classical]) 1)); -val Var_elim2 = result(); +qed "Var_elim2"; goal Subst.thy "v : vars_of(t <| s) --> v : srange(s) | v : vars_of(t)"; by (uterm_ind_tac "t" 1); @@ -166,20 +166,20 @@ by (etac notE 1); by (etac subst 1); by (ALLGOALS (fast_tac set_cs)); -val Var_intro = result() RS mp; +val Var_intro = store_thm("Var_intro", result() RS mp); goal Subst.thy "v : srange(s) --> (? w.w : sdom(s) & v : vars_of(Var(w) <| s))"; by (simp_tac (subst_ss addsimps [srange_iff]) 1); -val srangeE = make_elim (result() RS mp); +val srangeE = store_thm("srangeE", make_elim (result() RS mp)); val asms = goal Subst.thy "sdom(s) Int srange(s) = {} = (! t.sdom(s) Int vars_of(t <| s) = {})"; by (simp_tac subst_ss 1); by (fast_tac (set_cs addIs [Var_elim2] addEs [srangeE]) 1); -val dom_range_disjoint = result(); +qed "dom_range_disjoint"; val asms = goal Subst.thy "~ u <| s = u --> (? x.x : sdom(s))"; by (simp_tac (subst_ss addsimps [invariance]) 1); by (fast_tac set_cs 1); -val subst_not_empty = result() RS mp; +val subst_not_empty = store_thm("subst_not_empty", result() RS mp);