Theorems · Theorem · commutative algebra

HomogeneousSubmodule.mk.congr_simp

∀ {ιA : Type u_1} {ιM : Type u_2} {σA : Type u_3} {σM : Type u_4} {A : Type u_5} {M : Type u_6} [inst : Semiring A]
  [inst_1 : AddCommMonoid M] [inst_2 : Module A M] {𝒜 : ιA → σA} {ℳ : ιM → σM} [inst_3 : DecidableEq ιA]
  [inst_4 : AddMonoid ιA] [inst_5 : SetLike σA A] [inst_6 : AddSubmonoidClass σA A] [inst_7 : GradedRing 𝒜]
  [inst_8 : DecidableEq ιM] [inst_9 : SetLike σM M] [inst_10 : AddSubmonoidClass σM M]
  [inst_11 : DirectSum.Decomposition ℳ] [inst_12 : VAdd ιA ιM] [inst_13 : SetLike.GradedSMul 𝒜 ℳ]
  (toSubmodule toSubmodule_1 : Submodule A M) (e_toSubmodule : toSubmodule = toSubmodule_1)
  (is_homogeneous' : toSubmodule.IsHomogeneous ℳ),
  { toSubmodule := toSubmodule, is_homogeneous' := is_homogeneous' } =
    { toSubmodule := toSubmodule_1, is_homogeneous' := ⋯ }

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleDecidableEqAddMonoidSetLikeAddSubmonoidClassGradedRingDecidableEqSetLikeAddSubmonoidClassDirectSum.DecompositionVAddSetLike.GradedSMul