diff options
Diffstat (limited to 'theories/Relations/Operators_Properties.v')
| -rwxr-xr-x | theories/Relations/Operators_Properties.v | 14 |
1 files changed, 6 insertions, 8 deletions
diff --git a/theories/Relations/Operators_Properties.v b/theories/Relations/Operators_Properties.v index d7cb7a7eb..0ca819b84 100755 --- a/theories/Relations/Operators_Properties.v +++ b/theories/Relations/Operators_Properties.v @@ -39,9 +39,9 @@ Lemma clos_rt_idempotent: (incl (clos_refl_trans A (clos_refl_trans A R)) (clos_refl_trans A R)). Red. -Induction 1; Auto with sets. +NewInduction 1; Auto with sets. Intros. -Apply rt_trans with y0; Auto with sets. +Apply rt_trans with y; Auto with sets. Qed. Lemma clos_refl_trans_ind_left: (A:Set)(R:A->A->Prop)(M:A)(P:A->Prop) @@ -72,9 +72,8 @@ Section Clos_Refl_Sym_Trans. Lemma clos_rt_clos_rst: (inclusion A (clos_refl_trans A R) (clos_refl_sym_trans A R)). Red. -Induction 1; Auto with sets. -Intros. -Apply rst_trans with y0; Auto with sets. +NewInduction 1; Auto with sets. +Apply rst_trans with y; Auto with sets. Qed. Lemma clos_rst_is_equiv: (equivalence A (clos_refl_sym_trans A R)). @@ -90,9 +89,8 @@ Qed. (incl (clos_refl_sym_trans A (clos_refl_sym_trans A R)) (clos_refl_sym_trans A R)). Red. -Induction 1; Auto with sets. -Intros. -Apply rst_trans with y0; Auto with sets. +NewInduction 1; Auto with sets. +Apply rst_trans with y; Auto with sets. Qed. End Clos_Refl_Sym_Trans. |