isAdjointPair_unique_of_nondegenerate

English

Equivalence of nondegeneracy under congruence: (congr e B).Nondegenerate ↔ B.Nondegenerate.

Русский

Эквивалентность неdegenerate при конгруэнции: (congr e B).Nondegenerate ↔ B.Nondegenerate.

LaTeX

$$$\\text{nondegenerate\_iff\_ }(congr e) \\; B$$$

Lean4

theorem isAdjointPair_unique_of_nondegenerate (B : BilinForm R₁ M₁) (b : B.Nondegenerate) (φ ψ₁ ψ₂ : M₁ →ₗ[R₁] M₁)
    (hψ₁ : IsAdjointPair B B ψ₁ φ) (hψ₂ : IsAdjointPair B B ψ₂ φ) : ψ₁ = ψ₂ :=
  B.compLeft_injective b <| ext fun v w => by rw [compLeft_apply, compLeft_apply, hψ₁, hψ₂]

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