isIsometricSMul'' — Mathlib

English

The same componentwise isometric action extends to the product type, confirming IsIsometricSMul for the product in the opposite form.

Русский

Та же компонентная изометрическая victime действует на произведении.

LaTeX

$$$\text{IsIsometricSMul}(M\times N, X\times Y)$ holds componentwise$$

Lean4

@[to_additive]
instance isIsometricSMul'' {N} [Mul M] [PseudoEMetricSpace M] [IsIsometricSMul Mᵐᵒᵖ M] [Mul N] [PseudoEMetricSpace N]
    [IsIsometricSMul Nᵐᵒᵖ N] : IsIsometricSMul (M × N)ᵐᵒᵖ (M × N) :=
  ⟨fun c => (isometry_mul_right c.unop.1).prodMap (isometry_mul_right c.unop.2)⟩

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