factor_comp_apply — Mathlib

English

If p is the kernel of f, then ker (p.liftQ f h) = ⊥, expressed via a reformulation with h derived from equality p = ker f.

Русский

Если p = ker f, то ker (p.liftQ f h) = ⊥, выражение через h, полученное из равенства p = ker f.

LaTeX

$$$$ \\ker (p.liftQ f h) = \\bot. $$$$

Lean4

@[simp]
theorem factor_comp_apply (H1 : p ≤ p') (H2 : p' ≤ p'') (x : M ⧸ p) :
    factor H2 (factor H1 x) = factor (H1.trans H2) x :=
  by
  rw [← comp_apply]
  simp

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