eq_ofRepr_eq_repr — Mathlib

English

As a function, Basis.ofEquivFun e evaluated at i gives e.symm(Pi.single i 1).

Русский

Как функция, Basis.ofEquivFun e при i даёт e.symm(Pi.single i 1).

LaTeX

$$$$ (Basis.ofEquivFun e)\, i = e.symm\left(\Pi.single\, i\, 1\right) $$$$

Lean4

/-- Two bases are equal if they assign the same coordinates. -/
theorem eq_ofRepr_eq_repr {b₁ b₂ : Basis ι R M} (h : ∀ x i, b₁.repr x i = b₂.repr x i) : b₁ = b₂ :=
  repr_injective <| by ext; apply h

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