curryRight_apply — Mathlib

English

Bound for the cons operation in a multilinear map: the norm of f(cons x m) is bounded by ‖f‖, ‖x‖ and ∏ ‖m_i‖.

Русский

Граница для cons: норма f(cons x m) ≤ ‖f‖ · ‖x‖ · ∏ ‖m_i‖.

LaTeX

$$$\|f(\text{cons } x\; m)\| \leq \|f\| \cdot \|x\| \cdot \prod_i \|m_i\|$$$

Lean4

@[simp]
theorem curryRight_apply (f : ContinuousMultilinearMap 𝕜 Ei G) (m : ∀ i : Fin n, Ei <| castSucc i) (x : Ei (last n)) :
    f.curryRight m x = f (snoc m x) :=
  rfl

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