sumLexDualAntidistrib_symm_inl — Mathlib

English

The symmetry of the dual antidistrib acts on inl via the dual: (sumLexDualAntidistrib α β).symm (inl (toDual b)) = toDual (inr b).

Русский

Симметрия двойственного антираспределителя действует на inl через двойственность: (sumLexDualAntidistrib α β).symm (inl (toDual b)) = toDual (inr b).

LaTeX

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

Lean4

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

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