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Diffstat (limited to 'theories/Init/Peano.v')
| -rw-r--r-- | theories/Init/Peano.v | 8 |
1 files changed, 1 insertions, 7 deletions
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v index f449d8383..216ca35af 100644 --- a/theories/Init/Peano.v +++ b/theories/Init/Peano.v @@ -50,13 +50,7 @@ Qed. (** Injectivity of successor *) -Theorem eq_add_S : forall n m:nat, S n = S m -> n = m. -Proof. - intros n m Sn_eq_Sm. - replace (n=m) with (pred (S n) = pred (S m)) by auto using pred_Sn. - rewrite Sn_eq_Sm; trivial. -Qed. - +Definition eq_add_S n m (H: S n = S m): n = m := f_equal pred H. Hint Immediate eq_add_S: core. Theorem not_eq_S : forall n m:nat, n <> m -> S n <> S m. |