Theorems · Theorem · ring theory
AddMonoidAlgebra.single_add_apply_of_not_exists_add
Deprecated since 2026-06-18Use AddMonoidAlgebra.coeff_single_mul_of_forall_add_ne instead.
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : Add M] (r : R) {g g' : M} (x : AddMonoidAlgebra R M),
(¬∃ d, g' = g + d) → (AddMonoidAlgebra.single g r * x).coeff g' = 0- Defined in
- Mathlib.Algebra.MonoidAlgebra.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsuppstatement · cited by 5,255
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffstatement · cited by 365
- AddMonoidAlgebra.singlestatement · cited by 250
- AddMonoidAlgebra.coeff_single_mul_of_forall_add_neproof · cited by 3
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