instZero — Mathlib

English

For f: continuous multilinear map to a product, f = g.prod h iff the projections fst ∘ f = g and snd ∘ f = h.

Русский

Для отображения f: M1 → (M2×M3) верно: f = g.prod h тогда и только тогда, когда fst ∘ f = g и snd ∘ f = h.

LaTeX

$$$f = g.\text{prod} h \iff (\text{fst}.\!\circ f) = g \wedge (\text{snd}.\!\circ f) = h$$$

Lean4

instance : Zero (ContinuousMultilinearMap R M₁ M₂) :=
  ⟨{ (0 : MultilinearMap R M₁ M₂) with cont := continuous_const }⟩

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