comp_add — Mathlib

English

The composition in the second argument is additive: z1 ∘ (z2 + z2') = z1 ∘ z2 + z1 ∘ z2'.

Русский

Компоновка по второй координате радикально аддитивна: z1 ∘ (z2 + z2') = z1 ∘ z2 + z1 ∘ z2'.

LaTeX

$$$\\forall z_1, z_2, z_2', h,\\ z_1 \\circ (z_2 + z_2') \\\\; h = z_1 \\circ z_2 \\\\; h + z_1 \\circ z_2' \\\\; h.$$$

Lean4

@[simp]
protected theorem comp_add {n₁ n₂ n₁₂ : ℤ} (z₁ : Cochain F G n₁) (z₂ z₂' : Cochain G K n₂) (h : n₁ + n₂ = n₁₂) :
    z₁.comp (z₂ + z₂') h = z₁.comp z₂ h + z₁.comp z₂' h :=
  by
  ext p q hpq
  simp only [comp_v _ _ h p _ q rfl (by cutsat), add_v, comp_add]

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