sumLexDualAntidistrib_symm_inr — Mathlib

English

The symmetry of the dual antidistrib on inr maps to the dual of inl: (sumLexDualAntidistrib α β).symm (inr (toDual a)) = toDual (inl a).

Русский

Симметрия двойственного антираспределителя по инр отображает в двойственность от инл: (sumLexDualAntidistrib α β).symm (inr (toDual a)) = toDual (inl a).

LaTeX

$$$\\bigl(\\text{sumLexDualAntidistrib}_{\\alpha,\\beta}\\bigr).symm(\\mathrm{inr}(\\mathrm{toDual}(a))) = \\mathrm{toDual}(\\mathrm{inl}(a))$$$

Lean4

@[simp]
theorem sumLexDualAntidistrib_symm_inr : (sumLexDualAntidistrib α β).symm (inr (toDual a)) = toDual (inl a) :=
  rfl

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