Theorems · Definition · commutative algebra

HomogeneousSubsemiring.mk.noConfusion

{ι : Type u_1} →
  {σ : Type u_2} →
    {A : Type u_3} →
      {inst : AddMonoid ι} →
        {inst_1 : Semiring A} →
          {inst_2 : SetLike σ A} →
            {inst_3 : AddSubmonoidClass σ A} →
              {𝒜 : ι → σ} →
                {inst_4 : DecidableEq ι} →
                  {inst_5 : GradedRing 𝒜} →
                    {P : Sort u} →
                      {toSubsemiring : Subsemiring A} →
                        {is_homogeneous' : DirectSum.SetLike.IsHomogeneous 𝒜 toSubsemiring} →
                          {toSubsemiring' : Subsemiring A} →
                            {is_homogeneous'' : DirectSum.SetLike.IsHomogeneous 𝒜 toSubsemiring'} →
                              { toSubsemiring := toSubsemiring, is_homogeneous' := is_homogeneous' } =
                                  { toSubsemiring := toSubsemiring', is_homogeneous' := is_homogeneous'' } →
                                (toSubsemiring ≍ toSubsemiring' → P) → P

Defined in

Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound