Theorems · Theorem · general algebraic systems
Finsupp.mapDomain_apply
∀ {α : Type u_1} {β : Type u_2} {M : Type u_5} [inst : AddCommMonoid M] {f : α → β},
Function.Injective f → ∀ (x : α →₀ M) (a : α), (Finsupp.mapDomain f x) (f a) = x a- Defined in
- Mathlib.Data.Finsupp.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finsupp.single_eq_sameproof · cited by 171
- Finsupp.mapDomainstatement · cited by 168
- Pi.zero_applyproof · cited by 70
- Finsupp.single_zeroproof · cited by 63
- Finsupp.single_eq_of_ne'proof · cited by 36
- Finsupp.sum_applyproof · cited by 27
- Finsupp.sum_eq_singleproof · cited by 18
- Finsupp.coe_zeroproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- Finsupp.mapDomain_injectiveproof · cited by 16
- Finsupp.mapDomain_equiv_applyproof · cited by 15
- Finsupp.embDomain_eq_mapDomainproof · cited by 13
- Representation.coeff_ofMulActionproof · cited by 4
- Finsupp.comapDomain_mapDomainproof · cited by 1
- Finsupp.support_mapDomain_embeddingproof · cited by 1
- Algebra.Generators.toComp_toAlgHom_monomialproof · cited by 1
- MvPolynomial.IsSymmetric.antitone_supDegreeproof · cited by 1
- Finsupp.sumElim_eq_addproof · cited by 1
- Finsupp.mapDomain_tsubproof · cited by 1
- Finsupp.comapSMul_applyproof · cited by 0