coe_inj — Mathlib

English

The coercion from Matroidᵣ α to Matroid α is injective: (M₁ : Matroid α) = (M₂ : Matroid α) iff M₁ = M₂.

Русский

Коэрцировка из Matroidᵣ α в Matroid α инъективна: (M₁ : Matroid α) = (M₂ : Matroid α) эквивалентно M₁ = M₂.

LaTeX

$$$ (M_1 : Matroid \\alpha) = (M_2 : Matroid \\alpha) \\iff M_1 = M_2 $$$

Lean4

@[simp]
theorem coe_inj {M₁ M₂ : Matroidᵣ α} : (M₁ : Matroid α) = (M₂ : Matroid α) ↔ M₁ = M₂ :=
  Matroidᵣ.ext_iff.symm

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