Theorems · Theorem · ring theory
MonoidAlgebra.map_injective
∀ {R : Type u_3} {S : Type u_4} {M : Type u_6} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+ S),
Function.Injective ⇑f → Function.Injective (MonoidAlgebra.map f)MonoidAlgebra.map of an injective function is injective.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.MapDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- Semiringstatement and proof · cited by 13,802
- Equiv.symmproof · cited by 3,681
- AddMonoidHomstatement and proof · cited by 3,230
- map_zeroproof · cited by 1,614
- MonoidAlgebrastatement and proof · cited by 590
- Finsupp.extproof · cited by 399
- MonoidAlgebra.coeffproof · cited by 224
- Finsupp.mapRangeproof · cited by 91
- MonoidAlgebra.extproof · cited by 78
- MonoidAlgebra.mapstatement and proof · cited by 17
- MonoidAlgebra.coeffEquivproof · cited by 12
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