adj_congr_of_sym2 — Mathlib

English

If G' is a subgraph and u,v are vertices of G' with G'.Adj u v, then G.Adj u v.

Русский

Если G' — подграф и u,v — вершины G' с G'.Adj u v, тогда G.Adj u v.

LaTeX

$$G'.Adj u v → G.Adj u v$$

Lean4

theorem adj_congr_of_sym2 {H : G.Subgraph} {u v w x : V} (h2 : s(u, v) = s(w, x)) : H.Adj u v ↔ H.Adj w x :=
  by
  simp only [Sym2.eq, Sym2.rel_iff', Prod.mk.injEq, Prod.swap_prod_mk] at h2
  rcases h2 with hl | hr
  · rw [hl.1, hl.2]
  · rw [hr.1, hr.2, Subgraph.adj_comm]

Похожие утверждения