sieve₁'_eq_sieve₁ — Mathlib

English

Equality of sieve1' and sieve1 follows from HasPullback structure.

Русский

Равенство sieve1' и sieve1 следует из структуры HasPullback.

LaTeX

$$$ E.sieve_1' i_1 i_2 = E.sieve_1( pullback.fst (E.f i_1) (E.f i_2), pullback.snd (E.f i_1) (E.f i_2) )$$$

Lean4

theorem sieve₁'_eq_sieve₁ : E.sieve₁' i₁ i₂ = E.sieve₁ (pullback.fst _ _) (pullback.snd _ _) :=
  by
  rw [← Sieve.pullback_id (S := E.sieve₁' i₁ i₂), sieve₁_eq_pullback_sieve₁' _ _ _ pullback.condition]
  congr
  cat_disch

Похожие утверждения