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[Merged by Bors] - feat(Logic/Function/Basic) : lemmas about composition of and in onFun #39776

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[Merged by Bors] - feat(Logic/Function/Basic) : lemmas about composition of and in onFun #39776

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6 changes: 6 additions & 0 deletions Mathlib/Logic/Function/Basic.lean
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Expand Up @@ -55,6 +55,12 @@ section onFun
theorem onFun_apply (f : β → β → γ) (g : α → β) (a b : α) : onFun f g a b = f (g a) (g b) :=
rfl

theorem onFun_onFun_eq {δ : Sort*} (f : α → α → γ) (g : β → α) (h : δ → β) :
(f.onFun g).onFun h = f.onFun (g ∘ h) := rfl

theorem onFun_comp_eq {δ : Sort*} (f : α → α → γ) (g : β → α) (h : δ → β) :
f.onFun (g ∘ h) = (f.onFun g).onFun h := rfl

variable (r : β → β → Prop) (f : α → β)

instance [Std.Refl r] : Std.Refl (r on f) where
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