Theorems · Theorem · linear algebra

LinearMap.prodOfFinsuppNat_injective

∀ {R : Type u_1} {M : Type u_2} {P : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid P] [inst_4 : Module R P] {f : P × M →ₗ[R] M},
  Function.Injective ⇑f → Function.Injective ⇑f.prodOfFinsuppNat

Defined in: Mathlib.LinearAlgebra.Finsupp.Pi
Cited by: 1 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module AddCommMonoid Module

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Cites26

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
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
Semiringstatement and proof · cited by 13,802
Finsetproof · cited by 13,712
AddCommMonoidstatement and proof · cited by 12,281
LinearMapstatement and proof · cited by 10,215
Finsuppstatement and proof · cited by 5,255
map_zeroproof · cited by 1,614
Finset.Nonemptyproof · cited by 1,001
Finsupp.singleproof · cited by 943
Finsupp.supportproof · cited by 828

Cited by1

Results whose statement or proof uses this declaration.

LinearMap.exists_finsupp_nat_of_prod_injectiveproof · cited by 2