Theorems · Theorem · ring theory
AddMonoidAlgebra.single_left_inj
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {r : R} {m₁ m₂ : M},
r ≠ 0 → (AddMonoidAlgebra.single m₁ r = AddMonoidAlgebra.single m₂ r ↔ m₁ = m₂)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddMonoidAlgebrastatement · cited by 649
- AddMonoidAlgebra.singlestatement · cited by 250
- AddMonoidAlgebra.single_injproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.single_left_injectiveproof · cited by 2
- MvPolynomial.monomial_left_injproof · cited by 0