Theorems · Theorem · ring theory
AddMonoidAlgebra.single_inj
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {r₁ r₂ : R} {m₁ m₂ : M},
AddMonoidAlgebra.single m₁ r₁ = AddMonoidAlgebra.single m₂ r₂ ↔ m₁ = m₂ ∧ r₁ = r₂ ∨ r₁ = 0 ∧ r₂ = 0- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 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.
Cites5
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
- Finsupp.single_eq_single_iffproof · cited by 6
- AddMonoidAlgebra.coeff_injproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.single_left_injproof · cited by 2
- AddMonoidAlgebra.single_right_injproof · cited by 1
- Polynomial.monomial_eq_monomial_iffproof · cited by 1
- MvPolynomial.monomial_eq_monomial_iffproof · cited by 1