spanSingleton_mul_spanSingleton — Mathlib

English

The product of spans corresponds to the span of the product.

Русский

Произведение спанов соответствует SpanSingleton от произведения.

LaTeX

$$$spanSingleton\\;S\\;x \\cdot spanSingleton\\;S\\;y = spanSingleton\\;S\\;(x y)$$$

Lean4

@[simp]
theorem spanSingleton_mul_spanSingleton (x y : P) : spanSingleton S x * spanSingleton S y = spanSingleton S (x * y) :=
  by
  apply coeToSubmodule_injective
  simp only [coe_mul, coe_spanSingleton, span_mul_span, singleton_mul_singleton]

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