basisFun_apply — Mathlib

English

The canonical function basisFun is equal to itself under the definitional equivalence; i.e., the basisFun is consistently identified with itself.

Русский

Канонический базис basisFun совпадает с самим собой under определенной эквивалентности.

LaTeX

$$$\text{basisFun } R η = \text{basisFun } R η$$$

Lean4

@[simp]
theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = Pi.single i 1 := by
  simp only [basisFun, Basis.coe_ofEquivFun, LinearEquiv.refl_symm, LinearEquiv.refl_apply]

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