toNonUnitalNonAssocSemiring_injective

English

Two NonUnitalNonAssocCommSemiring structures on R are equal if their additive and multiplicative data align.

Русский

Две структуры NonUnitalNonAssocCommSemiring на R равны, если их аддитивная и мультипликативная часть согласованы.

LaTeX

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

Lean4

theorem toNonUnitalNonAssocSemiring_injective : Function.Injective (@toNonUnitalNonAssocSemiring R) := by
  rintro ⟨⟩ ⟨⟩ _; congr

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