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pi8027/catIl.v

Last active June 21, 2020 20:39
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catIl.v
Require Import all_ssreflect.
Section cat.
Variable (A : Type).
Lemma catIr : right_injective (@cat A).
Proof. by elim => //= ? ? IH ? ? [] /IH. Qed.
Lemma catIl : left_injective (@cat A).
Proof.
by move=> ? ? ? /(f_equal rev); rewrite !rev_cat => /catIr /(inv_inj revK).
(* elim/last_ind => [? ?|? ? IH ? ?]; rewrite ?cats0 // -!rcons_cat. *)
(* by move/(@rcons_injl A)/IH. *)
Qed.
End cat.
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