orderIsoSumLexPUnit_toLex — Mathlib

English

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

Русский

Симметрия sumLexDualAntidistrib на inl переводит в двойственность инр: (sumLexDualAntidistrib α β).symm (toDual (inl a)) = toDual (inr a).

LaTeX

$$$\\bigl(\\text{sumLexDualAntidistrib}_{\\alpha,\\beta}\\bigr)^{-1}(\\mathrm{toDual}(\\mathrm{inl}(a))) = \\mathrm{toDual}(\\mathrm{inr}(a))$$$

Lean4

@[simp]
theorem orderIsoSumLexPUnit_toLex (a : α) : orderIsoSumLexPUnit ↑a = toLex (inl a) :=
  rfl

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