subsingleton_left — Mathlib

English

If Subalgebra R A is a singleton, then the type of AlgEquiv R A B is itself a subsingleton (i.e., any two such equivalences are equal).

Русский

Если Subalgebra R A — одноэлементная, то множество AlgEquiv R A B — единично。

LaTeX

$$$ \\mathrm{AlgEquiv.subsingleton_left} : [\\mathrm{Subsingleton} (\\mathrm{Subalgebra} R A)] \\Rightarrow \\mathrm{Subsingleton} (A \\simeq_{R} B) $$$

Lean4

instance _root_.AlgEquiv.subsingleton_left [Subsingleton (Subalgebra R A)] : Subsingleton (A ≃ₐ[R] B) :=
  ⟨fun f g => AlgEquiv.ext fun x => AlgHom.ext_iff.mp (Subsingleton.elim f.toAlgHom g.toAlgHom) x⟩

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