English
Let α be a monoid and consider a, x, y ∈ αᵐᵒᵖ. The semiconjugacy relation transfers via unop exactly: SemiconjBy (unop a) (unop y) (unop x) holds if and only if SemiconjBy a x y holds.
Русский
Пусть α — моноид и рассмотрим a, x, y ∈ αᵐᵒᵖ. Полу сопряжённость переносится через unop точно: SemiconjBy (unop a) (unop y) (unop x) эквивалентно SemiconjBy a x y.
LaTeX
$$$\\SemiconjBy\\ (\\operatorname{unop} a)\\ (\\operatorname{unop} y)\\ (\\operatorname{unop} x)\\ \\iff\\ \\SemiconjBy\\ a\\ x\\ y$$$
Lean4
@[to_additive (attr := simp, nolint simpComm)]
theorem semiconjBy_unop [Mul α] {a x y : αᵐᵒᵖ} : SemiconjBy (unop a) (unop y) (unop x) ↔ SemiconjBy a x y := by
conv_rhs => rw [← op_unop a, ← op_unop x, ← op_unop y, semiconjBy_op]
