Theorems · Definition · commutative algebra

HomogeneousSubmodule.recOn

{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] →
                                            {motive : HomogeneousSubmodule 𝒜 ℳ → Sort u} →
                                              (t : HomogeneousSubmodule 𝒜 ℳ) →
                                                ((toSubmodule : Submodule A M) →
                                                    (is_homogeneous' : toSubmodule.IsHomogeneous ℳ) →
                                                      motive
                                                        { toSubmodule := toSubmodule,
                                                          is_homogeneous' := is_homogeneous' }) →
                                                  motive t

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleDecidableEqAddMonoidSetLikeAddSubmonoidClassGradedRingDecidableEqSetLikeAddSubmonoidClassDirectSum.DecompositionVAddSetLike.GradedSMul