recolorOfCardLE — Mathlib

English

There is a noncomputable embedding recolorOfCardLE if |α| ≤ |β|, sending colorings of α to colorings of β.

Русский

Существует нескомпьютерная встраиваемость recolorOfCardLE при |α| ≤ |β|, отображающая раскраски α в раскраски β.

LaTeX

$$$Fintype.card \\alpha ≤ Fintype.card \\beta \\Rightarrow G.Coloring \\alpha \\hookrightarrow G.Coloring \\beta$$$

Lean4

/-- There is a noncomputable embedding of `α`-colorings to `β`-colorings if
`β` has at least as large a cardinality as `α`. -/
noncomputable def recolorOfCardLE {α β : Type*} [Fintype α] [Fintype β] (hn : Fintype.card α ≤ Fintype.card β) :
    G.Coloring α ↪ G.Coloring β :=
  G.recolorOfEmbedding <| (Function.Embedding.nonempty_of_card_le hn).some

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