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-rw-r--r--theories/Arith/PeanoNat.v10
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Arith/PeanoNat.v b/theories/Arith/PeanoNat.v
index 4e4938a99..bc58995fd 100644
--- a/theories/Arith/PeanoNat.v
+++ b/theories/Arith/PeanoNat.v
@@ -315,7 +315,7 @@ Import Private_Parity.
Lemma even_spec : forall n, even n = true <-> Even n.
Proof.
- fix 1.
+ fix even_spec 1.
destruct n as [|[|n]]; simpl.
- split; [ now exists 0 | trivial ].
- split; [ discriminate | intro H; elim (Even_1 H) ].
@@ -325,7 +325,7 @@ Qed.
Lemma odd_spec : forall n, odd n = true <-> Odd n.
Proof.
unfold odd.
- fix 1.
+ fix odd_spec 1.
destruct n as [|[|n]]; simpl.
- split; [ discriminate | intro H; elim (Odd_0 H) ].
- split; [ now exists 0 | trivial ].
@@ -473,7 +473,7 @@ Notation "( x | y )" := (divide x y) (at level 0) : nat_scope.
Lemma gcd_divide : forall a b, (gcd a b | a) /\ (gcd a b | b).
Proof.
- fix 1.
+ fix gcd_divide 1.
intros [|a] b; simpl.
split.
now exists 0.
@@ -502,7 +502,7 @@ Qed.
Lemma gcd_greatest : forall a b c, (c|a) -> (c|b) -> (c|gcd a b).
Proof.
- fix 1.
+ fix gcd_greatest 1.
intros [|a] b; simpl; auto.
fold (b mod (S a)).
intros c H H'. apply gcd_greatest; auto.
@@ -536,7 +536,7 @@ Qed.
Lemma le_div2 n : div2 (S n) <= n.
Proof.
revert n.
- fix 1.
+ fix le_div2 1.
destruct n; simpl; trivial. apply lt_succ_r.
destruct n; [simpl|]; trivial. now constructor.
Qed.