Theorems · Theorem · ring theory
AddMonoidAlgebra.mapDomain_comapDomain
∀ {R : Type u_3} {M : Type u_6} {N : Type u_7} [inst : Semiring R] {f : M → N} {x : AddMonoidAlgebra R N},
↑x.coeff.support ⊆ Set.range f →
∀ (hf : Function.Injective f), AddMonoidAlgebra.mapDomain f (AddMonoidAlgebra.comapDomain f hf x) = x- Defined in
- Mathlib.Algebra.MonoidAlgebra.MapDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- Finsupp.supportstatement and proof · cited by 828
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffstatement and proof · cited by 365
- AddMonoidAlgebra.extproof · cited by 90
- AddMonoidAlgebra.mapDomainstatement · cited by 17
- Finsupp.mapDomain_comapDomainproof · cited by 7
- AddMonoidAlgebra.comapDomainstatement · cited by 7
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