comp_appLE — Mathlib

English

The appLE of the composition equals the composition of apps: (f ≫ g).appLE U V e = g.app U ≫ f.appLE _ V e.

Русский

APPLE композиции равен композиции APPLE: (f ≫ g).appLE U V e = g.app U ≫ f.appLE _ V e.

LaTeX

$$$(f \\gg g).appLE U V e = g.app U \\circ f.appLE _ V e$$$

Lean4

@[simp, reassoc] -- reassoc lemma does not need `simp`

theorem comp_appLE {X Y Z : Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (U V e) : (f ≫ g).appLE U V e = g.app U ≫ f.appLE _ V e :=
  by rw [g.app_eq_appLE, appLE_comp_appLE]

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