fin3_def_ext — Mathlib

English

For any a, b, c ∈ R and P: Fin 3 → R, the evaluation of P at coordinates a, b, c yields the coordinates of the smoothed vector: (P a, P b, P c) correspond to the entries a, b, c respectively.

Русский

Для любых a, b, c ∈ R и P : Fin 3 → R значения P(a), P(b), P(c) образуют тройку координат: P(0)=a, P(1)=b, P(2)=c.

LaTeX

$$$(P x) = a ∧ (P y) = b ∧ (P z) = c$$$

Lean4

theorem fin3_def_ext (a b c : R) : ![a, b, c] x = a ∧ ![a, b, c] y = b ∧ ![a, b, c] z = c :=
  ⟨rfl, rfl, rfl⟩

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