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-rw-r--r--theories/Numbers/Cyclic/Int31/Cyclic31.v4
1 files changed, 2 insertions, 2 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v
index a5b537caa..1acdd17e5 100644
--- a/theories/Numbers/Cyclic/Int31/Cyclic31.v
+++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v
@@ -1692,7 +1692,7 @@ Section Int31_Specs.
unfold head031, recl.
change On with (phi_inv (Z_of_nat (31-size))).
replace (head031_alt size x) with
- (head031_alt size x + (31 - size))%nat by (apply plus_0_r; auto).
+ (head031_alt size x + (31 - size))%nat by auto.
assert (size <= 31)%nat by auto with arith.
revert x H; induction size; intros.
@@ -1800,7 +1800,7 @@ Section Int31_Specs.
unfold tail031, recr.
change On with (phi_inv (Z_of_nat (31-size))).
replace (tail031_alt size x) with
- (tail031_alt size x + (31 - size))%nat by (apply plus_0_r; auto).
+ (tail031_alt size x + (31 - size))%nat by auto.
assert (size <= 31)%nat by auto with arith.
revert x H; induction size; intros.