in₂₁_iff' — Mathlib

English

Alternative form of the γ-β edge criterion: there exists a triple in t realizing the edge between in2 c and in1 b.

Русский

Альтернативная форма критерий ребра γ-β: существует тройка в t, реализующая ребро в between in2 c и in1 b.

LaTeX

$$$(graph\\ t).Adj(\\mathrm{in}_2 c)(\\mathrm{in}_1 b) \\iff \\exists x=(a,b,c)\\in t, (b,c) coordinates align$$$

Lean4

theorem in₂₁_iff' : (graph t).Adj (in₂ c) (in₁ b) ↔ ∃ x : α × β × γ, x ∈ t ∧ x.2.2 = c ∧ x.2.1 = b
    where
  mp := by rintro ⟨⟩; exact ⟨_, ‹_›, by simp⟩
  mpr := by rintro ⟨⟨a, b, c⟩, h, rfl, rfl⟩; constructor; assumption

Похожие утверждения