Theorems · Theorem · ring theory
AddMonoidAlgebra.single_ne_zero
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] {r : R} {m : M}, AddMonoidAlgebra.single m r ≠ 0 ↔ r ≠ 0- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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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
- Iff.notproof · cited by 489
- AddMonoidAlgebra.singlestatement · cited by 250
- AddMonoidAlgebra.single_eq_zeroproof · cited by 2
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