induceHomOfLE — Mathlib

English

If φ = φ1, then the induced homomorphism from φ equals that from φ1.

Русский

Если φ = φ1, то индуцированный гомоморфизм от φ равен индуцированному от φ1.

LaTeX

$$$( φ = φ_1 ) \Rightarrow (\mathrm{induceHom} \ φ \ φ_{st}) = (\mathrm{induceHom} \ φ_1 \ φ_{st})$$$

Lean4

/-- Given an inclusion of vertex subsets, the induced embedding on induced graphs.
This is not an abbreviation for `induceHom` since we get an embedding in this case. -/
def induceHomOfLE (h : s ≤ s') : G.induce s ↪g G.induce s'
    where
  toEmbedding := Set.embeddingOfSubset s s' h
  map_rel_iff' := by simp

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