weakEquivalence_of_postcomp_of_fac

English

The symmetric version of the mk-preservation under the left-right equivalence sends mk(f) to mk(f).

Русский

Симметричное отображение mk сохраняет mk(f).

LaTeX

$$$\operatorname{leftHomotopyClassEquivRightHomotopyClass\}.\mathrm{symm}({\rm mk}(f)) = {\rm mk}(f)$$$

Lean4

theorem weakEquivalence_of_postcomp_of_fac (fac : f ≫ g = fg) [WeakEquivalence g] [hfg : WeakEquivalence fg] :
    WeakEquivalence f := by
  subst fac
  exact weakEquivalence_of_postcomp f g

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