equivOp — Mathlib

English

There is a natural bijection between any submonoid H of M and its opposite H^{op}.

Русский

Существует естественная биекции между подмоном же H ⊆ M и его противоположностью H^{op}.

LaTeX

$$$ \exists\, \text{equiv}: H \cong H^{op} \quad ( \text{for each } H \le M ) $$$

Lean4

/-- Bijection between a submonoid `H` and its opposite. -/
@[to_additive (attr := simps!) /-- Bijection between an additive submonoid `H` and its opposite. -/
    ]
def equivOp (H : Submonoid M) : H ≃ H.op :=
  MulOpposite.opEquiv.subtypeEquiv fun _ => Iff.rfl

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