ext — Mathlib

English

For NonUnitalNonAssocCommSemiring, the forgetful map from it to NonUnitalNonAssocSemiring is injective.

Русский

Для NonUnitalNonAssocCommSemiring отображение забывания к NonUnitalNonAssocSemiring инъективно.

LaTeX

$$$\\\\forall A,B \\,\\in \\, \\text{NonUnitalNonAssocCommSemiring}(R), \\\\ toNonUnitalNonAssocSemiring(A) = toNonUnitalNonAssocSemiring(B) \\\\Rightarrow A = B.$$$

Lean4

@[ext]
theorem ext ⦃inst₁ inst₂ : NonUnitalNonAssocCommSemiring R⦄ (h_add : local_hAdd[R, inst₁] = local_hAdd[R, inst₂])
    (h_mul : local_hMul[R, inst₁] = local_hMul[R, inst₂]) : inst₁ = inst₂ :=
  toNonUnitalNonAssocSemiring_injective <| NonUnitalNonAssocSemiring.ext h_add h_mul

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