p_descOpcycles — Mathlib

English

The composition of pOpcycles with descOpcycles equals the original map: K.pOpcycles i ≫ K.descOpcycles k j hj hk = k.

Русский

Согласование pOpcycles и descOpcycles: K.pOpcycles i ∘ K.descOpcycles k j hj hk = k.

LaTeX

$$$K.pOpcycles i \circ K.descOpcycles k j hj hk = k$$$

Lean4

@[reassoc (attr := simp)]
theorem p_descOpcycles {A : C} (k : K.X i ⟶ A) (j : ι) (hj : c.prev i = j) (hk : K.d j i ≫ k = 0) :
    K.pOpcycles i ≫ K.descOpcycles k j hj hk = k :=
  by
  dsimp [descOpcycles, pOpcycles]
  simp

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