Commit 0ce29e73 authored by Robbert Krebbers's avatar Robbert Krebbers
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Merge branch 'mod-uniform' into 'master'

Future proof rotate_nat_add_add_mod

See merge request iris/stdpp!240
parents c1266011 89c50de2
......@@ -1208,20 +1208,12 @@ on nat since otherwise we need the sidecondition [base < len] on
Definition rotate_nat_sub (base offset len : nat) : nat :=
Z.to_nat ((len + offset - base) `mod` len)%Z.
Lemma rotate_nat_add_len_0 base offset:
rotate_nat_add base offset 0 = 0.
Proof. unfold rotate_nat_add. by rewrite Zmod_0_r. Qed.
Lemma rotate_nat_sub_len_0 base offset:
rotate_nat_sub base offset 0 = 0.
Proof. unfold rotate_nat_sub. by rewrite Zmod_0_r. Qed.
Lemma rotate_nat_add_add_mod base offset len:
rotate_nat_add base offset len =
rotate_nat_add (Z.to_nat (base `mod` len)%Z) offset len.
Proof.
destruct len as [|i];[ by rewrite !rotate_nat_add_len_0|].
pose proof (Z_mod_lt base (S i)) as Hlt. unfold rotate_nat_add.
rewrite !Z2Nat.id by lia. by rewrite Zplus_mod_idemp_l.
unfold rotate_nat_add. rewrite !Z2Nat.id; [by rewrite Zplus_mod_idemp_l|].
destruct len as [|i]; [rewrite Zmod_0_r|apply Z_mod_lt]; lia.
Qed.
Lemma rotate_nat_add_alt base offset len:
......
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