ext_ring — Mathlib

English

As before, the extensional principle for restricted argument forms yields equality from equality at a distinguished input.

Русский

Как и ранее, принцип экстренсионности по особому входу даёт равенство по значимому аргументу.

LaTeX

$$f(1) = g(1) ⇒ f = g$$

Lean4

/-- If two continuous `R`-multilinear maps from `R` are equal on 1, then they are equal.

This is the multilinear version of `ContinuousLinearMap.ext_ring`. -/
@[ext]
theorem ext_ring [Finite ι] [TopologicalSpace R] ⦃f g : ContinuousMultilinearMap R (fun _ : ι => R) M₂⦄
    (h : f (fun _ ↦ 1) = g (fun _ ↦ 1)) : f = g :=
  toMultilinearMap_injective <| MultilinearMap.ext_ring h

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