| author | wenzelm |
| Tue, 13 Jun 2006 23:41:39 +0200 | |
| changeset 19876 | 11d447d5d68c |
| parent 17274 | 746bb4c56800 |
| child 21669 | c68717c16013 |
| permissions | -rw-r--r-- |
| 2441 | 1 |
(* Title: HOL/Nat.ML |
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ID: $Id$ |
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*) |
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||
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(** legacy ML bindings **) |
|
5188
633ec5f6c155
Declaration of type 'nat' as a datatype (this allows usage of
berghofe
parents:
5069
diff
changeset
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|
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structure nat = |
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struct |
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val distinct = thms "nat.distinct"; |
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val inject = thms "nat.inject"; |
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val exhaust = thm "nat.exhaust"; |
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val cases = thms "nat.cases"; |
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val split = thm "nat.split"; |
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val split_asm = thm "nat.split_asm"; |
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val induct = thm "nat.induct"; |
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val recs = thms "nat.recs"; |
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val simps = thms "nat.simps"; |
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end; |
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val [nat_rec_0, nat_rec_Suc] = thms "nat.recs"; |
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bind_thm ("nat_rec_0", nat_rec_0);
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bind_thm ("nat_rec_Suc", nat_rec_Suc);
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|
5188
633ec5f6c155
Declaration of type 'nat' as a datatype (this allows usage of
berghofe
parents:
5069
diff
changeset
|
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val [nat_case_0, nat_case_Suc] = thms "nat.cases"; |
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bind_thm ("nat_case_0", nat_case_0);
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bind_thm ("nat_case_Suc", nat_case_Suc);
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|
5188
633ec5f6c155
Declaration of type 'nat' as a datatype (this allows usage of
berghofe
parents:
5069
diff
changeset
|
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val leD = thm "leD"; (*Now defined in Orderings.thy*) |
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val leI = thm "leI"; |
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||
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val Least_Suc = thm "Least_Suc"; |
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val Least_Suc2 = thm "Least_Suc2"; |
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val One_nat_def = thm "One_nat_def"; |
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val Suc_Suc_eq = thm "Suc_Suc_eq"; |
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val Suc_def = thm "Suc_def"; |
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val Suc_diff_diff = thm "Suc_diff_diff"; |
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val Suc_diff_le = thm "Suc_diff_le"; |
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val Suc_inject = thm "Suc_inject"; |
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val Suc_leD = thm "Suc_leD"; |
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val Suc_leI = thm "Suc_leI"; |
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val Suc_le_D = thm "Suc_le_D"; |
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val Suc_le_eq = thm "Suc_le_eq"; |
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val Suc_le_lessD = thm "Suc_le_lessD"; |
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val Suc_le_mono = thm "Suc_le_mono"; |
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val Suc_lessD = thm "Suc_lessD"; |
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val Suc_lessE = thm "Suc_lessE"; |
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val Suc_lessI = thm "Suc_lessI"; |
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val Suc_less_SucD = thm "Suc_less_SucD"; |
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val Suc_less_eq = thm "Suc_less_eq"; |
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val Suc_mono = thm "Suc_mono"; |
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val Suc_mult_cancel1 = thm "Suc_mult_cancel1"; |
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val Suc_mult_le_cancel1 = thm "Suc_mult_le_cancel1"; |
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val Suc_mult_less_cancel1 = thm "Suc_mult_less_cancel1"; |
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val Suc_n_not_le_n = thm "Suc_n_not_le_n"; |
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val Suc_n_not_n = thm "Suc_n_not_n"; |
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val Suc_neq_Zero = thm "Suc_neq_Zero"; |
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val Suc_not_Zero = thm "Suc_not_Zero"; |
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val Suc_pred = thm "Suc_pred"; |
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val Zero_nat_def = thm "Zero_nat_def"; |
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val Zero_neq_Suc = thm "Zero_neq_Suc"; |
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val Zero_not_Suc = thm "Zero_not_Suc"; |
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val add_0 = thm "add_0"; |
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val add_0_right = thm "add_0_right"; |
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val add_Suc = thm "add_Suc"; |
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val add_Suc_right = thm "add_Suc_right"; |
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val add_ac = thms "add_ac"; |
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val add_assoc = thm "add_assoc"; |
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val add_commute = thm "add_commute"; |
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val add_diff_inverse = thm "add_diff_inverse"; |
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val add_eq_self_zero = thm "add_eq_self_zero"; |
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val add_gr_0 = thm "add_gr_0"; |
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val add_is_0 = thm "add_is_0"; |
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val add_is_1 = thm "add_is_1"; |
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val add_leD1 = thm "add_leD1"; |
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val add_leD2 = thm "add_leD2"; |
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val add_leE = thm "add_leE"; |
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val add_le_mono = thm "add_le_mono"; |
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val add_le_mono1 = thm "add_le_mono1"; |
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val nat_add_left_cancel = thm "nat_add_left_cancel"; |
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val nat_add_left_cancel_le = thm "nat_add_left_cancel_le"; |
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val nat_add_left_cancel_less = thm "nat_add_left_cancel_less"; |
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val add_left_commute = thm "add_left_commute"; |
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val add_lessD1 = thm "add_lessD1"; |
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val add_less_mono = thm "add_less_mono"; |
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val add_less_mono1 = thm "add_less_mono1"; |
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val add_mult_distrib = thm "add_mult_distrib"; |
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val add_mult_distrib2 = thm "add_mult_distrib2"; |
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val nat_add_right_cancel = thm "nat_add_right_cancel"; |
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val def_nat_rec_0 = thm "def_nat_rec_0"; |
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val def_nat_rec_Suc = thm "def_nat_rec_Suc"; |
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val diff_0 = thm "diff_0"; |
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val diff_0_eq_0 = thm "diff_0_eq_0"; |
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val diff_Suc = thm "diff_Suc"; |
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val diff_Suc_Suc = thm "diff_Suc_Suc"; |
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val diff_Suc_less = thm "diff_Suc_less"; |
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val diff_add_0 = thm "diff_add_0"; |
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val diff_add_assoc = thm "diff_add_assoc"; |
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val diff_add_assoc2 = thm "diff_add_assoc2"; |
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val diff_add_inverse = thm "diff_add_inverse"; |
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val diff_add_inverse2 = thm "diff_add_inverse2"; |
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val diff_cancel = thm "diff_cancel"; |
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val diff_cancel2 = thm "diff_cancel2"; |
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val diff_commute = thm "diff_commute"; |
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val diff_diff_left = thm "diff_diff_left"; |
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val diff_induct = thm "diff_induct"; |
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val diff_is_0_eq = thm "diff_is_0_eq"; |
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val diff_le_self = thm "diff_le_self"; |
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val diff_less_Suc = thm "diff_less_Suc"; |
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val diff_mult_distrib = thm "diff_mult_distrib"; |
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val diff_mult_distrib2 = thm "diff_mult_distrib2"; |
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val diff_self_eq_0 = thm "diff_self_eq_0"; |
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val eq_imp_le = thm "eq_imp_le"; |
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val gr0I = thm "gr0I"; |
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val gr0_conv_Suc = thm "gr0_conv_Suc"; |
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val gr_implies_not0 = thm "gr_implies_not0"; |
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val inj_Suc = thm "inj_Suc"; |
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val le0 = thm "le0"; |
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val le_0_eq = thm "le_0_eq"; |
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val le_SucE = thm "le_SucE"; |
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val le_SucI = thm "le_SucI"; |
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val le_Suc_eq = thm "le_Suc_eq"; |
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val le_add1 = thm "le_add1"; |
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val le_add2 = thm "le_add2"; |
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val le_add_diff_inverse = thm "le_add_diff_inverse"; |
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val le_add_diff_inverse2 = thm "le_add_diff_inverse2"; |
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val le_anti_sym = thm "le_anti_sym"; |
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val le_def = thm "le_def"; |
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val le_eq_less_or_eq = thm "le_eq_less_or_eq"; |
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val le_imp_diff_is_add = thm "le_imp_diff_is_add"; |
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val le_imp_less_Suc = thm "le_imp_less_Suc"; |
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val le_imp_less_or_eq = thm "le_imp_less_or_eq"; |
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val le_less_trans = thm "le_less_trans"; |
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val le_neq_implies_less = thm "le_neq_implies_less"; |
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val le_refl = thm "le_refl"; |
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val le_simps = thms "le_simps"; |
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val le_trans = thm "le_trans"; |
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val lessE = thm "lessE"; |
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val lessI = thm "lessI"; |
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val less_Suc0 = thm "less_Suc0"; |
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val less_SucE = thm "less_SucE"; |
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val less_SucI = thm "less_SucI"; |
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val less_Suc_eq = thm "less_Suc_eq"; |
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val less_Suc_eq_0_disj = thm "less_Suc_eq_0_disj"; |
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val less_Suc_eq_le = thm "less_Suc_eq_le"; |
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val less_add_Suc1 = thm "less_add_Suc1"; |
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val less_add_Suc2 = thm "less_add_Suc2"; |
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val less_add_eq_less = thm "less_add_eq_less"; |
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val less_asym = thm "less_asym"; |
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val less_def = thm "less_def"; |
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val less_eq = thm "less_eq"; |
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val less_iff_Suc_add = thm "less_iff_Suc_add"; |
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val less_imp_Suc_add = thm "less_imp_Suc_add"; |
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val less_imp_add_positive = thm "less_imp_add_positive"; |
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val less_imp_diff_less = thm "less_imp_diff_less"; |
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val less_imp_le = thm "less_imp_le"; |
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val less_irrefl = thm "less_irrefl"; |
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val less_le_trans = thm "less_le_trans"; |
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val less_linear = thm "less_linear"; |
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val less_mono_imp_le_mono = thm "less_mono_imp_le_mono"; |
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val less_not_refl = thm "less_not_refl"; |
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val less_not_refl2 = thm "less_not_refl2"; |
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val less_not_refl3 = thm "less_not_refl3"; |
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val less_not_sym = thm "less_not_sym"; |
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val less_one = thm "less_one"; |
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val less_or_eq_imp_le = thm "less_or_eq_imp_le"; |
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val less_trans = thm "less_trans"; |
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val less_trans_Suc = thm "less_trans_Suc"; |
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val less_zeroE = thm "less_zeroE"; |
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val max_0L = thm "max_0L"; |
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val max_0R = thm "max_0R"; |
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val max_Suc_Suc = thm "max_Suc_Suc"; |
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val min_0L = thm "min_0L"; |
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val min_0R = thm "min_0R"; |
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val min_Suc_Suc = thm "min_Suc_Suc"; |
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val mult_0 = thm "mult_0"; |
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val mult_0_right = thm "mult_0_right"; |
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val mult_1 = thm "mult_1"; |
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val mult_1_right = thm "mult_1_right"; |
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val mult_Suc = thm "mult_Suc"; |
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val mult_Suc_right = thm "mult_Suc_right"; |
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val mult_ac = thms "mult_ac"; |
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val mult_assoc = thm "mult_assoc"; |
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val mult_cancel1 = thm "mult_cancel1"; |
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val mult_cancel2 = thm "mult_cancel2"; |
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val mult_commute = thm "mult_commute"; |
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val mult_eq_1_iff = thm "mult_eq_1_iff"; |
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val mult_eq_self_implies_10 = thm "mult_eq_self_implies_10"; |
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val mult_is_0 = thm "mult_is_0"; |
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val mult_le_cancel1 = thm "mult_le_cancel1"; |
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val mult_le_cancel2 = thm "mult_le_cancel2"; |
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val mult_le_mono = thm "mult_le_mono"; |
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val mult_le_mono1 = thm "mult_le_mono1"; |
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val mult_le_mono2 = thm "mult_le_mono2"; |
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val mult_left_commute = thm "mult_left_commute"; |
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val mult_less_cancel1 = thm "mult_less_cancel1"; |
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val mult_less_cancel2 = thm "mult_less_cancel2"; |
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val mult_less_mono1 = thm "mult_less_mono1"; |
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val mult_less_mono2 = thm "mult_less_mono2"; |
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val n_not_Suc_n = thm "n_not_Suc_n"; |
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val nat_distrib = thms "nat_distrib"; |
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val nat_induct = thm "nat_induct"; |
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val nat_induct2 = thm "nat_induct2"; |
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val nat_le_linear = thm "nat_le_linear"; |
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val nat_less_cases = thm "nat_less_cases"; |
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val nat_less_induct = thm "nat_less_induct"; |
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val nat_less_le = thm "nat_less_le"; |
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val nat_neq_iff = thm "nat_neq_iff"; |
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val nat_not_singleton = thm "nat_not_singleton"; |
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val neq0_conv = thm "neq0_conv"; |
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val not0_implies_Suc = thm "not0_implies_Suc"; |
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val not_add_less1 = thm "not_add_less1"; |
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val not_add_less2 = thm "not_add_less2"; |
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val not_gr0 = thm "not_gr0"; |
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val not_leE = thm "not_leE"; |
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val not_less0 = thm "not_less0"; |
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val not_less_eq = thm "not_less_eq"; |
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val not_less_less_Suc_eq = thm "not_less_less_Suc_eq"; |
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val not_less_simps = thms "not_less_simps"; |
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val one_eq_mult_iff = thm "one_eq_mult_iff"; |
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val one_is_add = thm "one_is_add"; |
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val one_le_mult_iff = thm "one_le_mult_iff"; |
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val one_reorient = thm "one_reorient"; |
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val pred_nat_def = thm "pred_nat_def"; |
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val trans_le_add1 = thm "trans_le_add1"; |
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val trans_le_add2 = thm "trans_le_add2"; |
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val trans_less_add1 = thm "trans_less_add1"; |
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val trans_less_add2 = thm "trans_less_add2"; |
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val wf_less = thm "wf_less"; |
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val wf_pred_nat = thm "wf_pred_nat"; |
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val zero_induct = thm "zero_induct"; |
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val zero_induct_lemma = thm "zero_induct_lemma"; |
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val zero_less_Suc = thm "zero_less_Suc"; |
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val zero_less_diff = thm "zero_less_diff"; |
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val zero_less_mult_iff = thm "zero_less_mult_iff"; |
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val zero_reorient = thm "zero_reorient"; |
|
|
17274
746bb4c56800
axclass: name space prefix is now "c_class" instead of just "c";
wenzelm
parents:
16796
diff
changeset
|
236 |
val linorder_neqE_nat = thm "linorder_neqE_nat"; |