Mathlib Map

Theorems · Theorem · ring theory

LinearMap.isLinear

∀ {R : Type u_1} {M : Type u_8} {M₂ : Type u_10} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (fₗ : M →ₗ[R] M₂), IsLinearMap R ⇑fₗ
Defined in
Mathlib.Algebra.Module.LinearMap.Defs
Cited by
10 results in Mathlib
Foundations
Depth 21 from the axioms · uses no axioms
Assumes
SemiringAddCommMonoidAddCommMonoidModuleModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousLinearMap.isBoundedLinearMap · cited by 6ContinuousLinearMap.isBou…LinearMap.image_convexHull · cited by 4LinearMap.image_convexHullIsBoundedLinearMap.snd · cited by 2IsBoundedLinearMap.sndIsBoundedLinearMap.add · cited by 2IsBoundedLinearMap.addIsBoundedLinearMap.fst · cited by 2IsBoundedLinearMap.fstIsBoundedLinearMap.id · cited by 2IsBoundedLinearMap.idIsBoundedLinearMap.neg · cited by 2IsBoundedLinearMap.negIsBoundedLinearMap.smul · cited by 0IsBoundedLinearMap.smulIsBoundedLinearMap.zero · cited by 0IsBoundedLinearMap.zeroIsBoundedLinearMap.comp · cited by 0IsBoundedLinearMap.compDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidLinearMap · cited by 10215LinearMapLinearMap.toAddHom · cited by 165LinearMap.toAddHomIsLinearMap · cited by 41IsLinearMapLinearMap.map_smul' · cited by 15LinearMap.map_smul'AddHom.map_add' · cited by 13AddHom.map_add'LinearMap.isLinearCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.