rcomap'_compose — Mathlib

English

The composition of rcomap' maps corresponds to the rcomap' map on the composed relation: Function composition equals the rcomap' along r ∘ s.

Русский

Сочетание функций rcomap' соответствует rcomap' на композицию: rcomap'(r) ∘ rcomap'(s) = rcomap'(r ∘ s).

LaTeX

$$$ \\mathrm{rcomp}'_{r} \\circ \\mathrm{rcomp}'_{s} = \\mathrm{rcomap}'_{r \\circ s} $$$

Lean4

@[simp]
theorem rcomap'_compose (r : SetRel α β) (s : SetRel β γ) : rcomap' r ∘ rcomap' s = rcomap' (r.comp s) :=
  funext <| rcomap'_rcomap' _ _

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