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Theorems · Theorem · ring theory

SetLike.IsHomogeneousElem.graded_smul

∀ {ιA : Type u_1} {ιB : Type u_2} {S : Type u_4} {R : Type u_5} {N : Type u_6} {M : Type u_7} [inst : SetLike S R]
  [inst_1 : SetLike N M] [inst_2 : VAdd ιA ιB] [inst_3 : SMul R M] {A : ιA → S} {B : ιB → N} [SetLike.GradedSMul A B]
  {a : R} {b : M}, SetLike.IsHomogeneousElem A a → SetLike.IsHomogeneousElem B b → SetLike.IsHomogeneousElem B (a • b)
Defined in
Mathlib.Algebra.GradedMulAction
Cited by
0 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
SetLikeSetLikeVAddSMulSetLike.GradedSMul
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HVAdd.hVAdd · cited by 1820HVAdd.hVAddSetLike · cited by 1084SetLikeVAdd · cited by 616VAddSetLike.IsHomogeneousElem · cited by 18SetLike.IsHomogeneousElemSetLike.GradedSMul · cited by 15SetLike.GradedSMulSetLike.GradedSMul.smul_mem · cited by 1GradedSMul.smul_memIsHomogeneousElem.graded_smulCITED BYCITES

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