parallelepiped_basisFun — Mathlib

English

A simp lemma about the Icc01 construction; trivial finite/true identities.

Русский

Простой факт о конструировании Icc01; тривиальные тождества.

LaTeX

$$$s^{\text{Finite}} \Rightarrow \text{True}$$$

Lean4

/-- The parallelepiped formed from the standard basis for `ι → ℝ` is `[0,1]^ι` -/
theorem parallelepiped_basisFun (ι : Type*) [Fintype ι] :
    (Pi.basisFun ℝ ι).parallelepiped = TopologicalSpace.PositiveCompacts.piIcc01 ι :=
  SetLike.coe_injective <|
    by
    refine Eq.trans ?_ ((uIcc_of_le ?_).trans (Set.pi_univ_Icc _ _).symm)
    · classical convert parallelepiped_single (ι := ι) 1
    · exact zero_le_one

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