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New lemmas: comp_idfunL, comp_idfunR. #1088

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strub merged 1 commit into from
Jul 25, 2026
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New lemmas: comp_idfunL, comp_idfunR. #1088

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8 changes: 8 additions & 0 deletions theories/core/Core.ec
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Expand Up @@ -150,6 +150,14 @@ proof. by move=> fK gK x y; rewrite -{1}[y]gK; apply (can_eq f g). qed.
lemma inj_idfun: injective (idfun<:'a>).
proof. by []. qed.

lemma comp_idfunL ['a 'b] (f : 'a -> 'b) : idfun \o f = f.
proof. by []. qed.

lemma comp_idfunR ['a 'b] (f : 'a -> 'b) : f \o idfun = f.
proof. by []. qed.

hint simplify comp_idfunL, comp_idfunR.

lemma inj_can_sym (f:'a -> 'b) f':
cancel f f' => injective f' => cancel f' f.
proof. by move=> fK injf' x; apply injf'; rewrite fK. qed.
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