Equiv_isup_symm_inclusion_apply — Mathlib

English

The inverse of the iSup equivalence applied to the inclusion map yields the i-th component application.

Русский

Обратная связь эквиваленции iSup применена к включению даёт i-ю компоненту.

LaTeX

$$$(\\mathrm{Equiv\_iSup} S)^{-1}\\bigl(\\mathrm{Substructure.inclusion}(\\mathrm{le\_iSup}\\ _\\ _) x\\bigr) = \\mathrm{of}_{L\\,\\iota\\ G\\ f,i} x.$$$

Lean4

theorem Equiv_isup_symm_inclusion_apply {i : ι} (x : S i) :
    (Equiv_iSup S).symm (Substructure.inclusion (le_iSup _ _) x) =
      of L ι _ (fun _ _ h ↦ Substructure.inclusion (S.monotone h)) i x :=
  by
  apply (Equiv_iSup S).injective
  simp only [Equiv.apply_symm_apply]
  rfl

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