isIsIsometricVAdd' — Mathlib

English

Same as above but in the Additive Mᵐᵒᵖ / M context with a reversed/alternate additive structure.

Русский

Аналогично в контексте Additive Mᵐᵒᵖ / M с развёрнутой структурой сложения.

LaTeX

$$$\\forall c \\in M, \\forall x,y:\\ edist(c \\cdot x, c \\cdot y) = edist(x,y).$$$

Lean4

instance isIsIsometricVAdd' [Mul M] [PseudoEMetricSpace M] [IsIsometricSMul M M] :
    IsIsometricVAdd (Additive M) (Additive M) :=
  ⟨fun c x y => edist_smul_left c.toMul x.toMul y.toMul⟩

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