Theorems · Theorem · commutative algebra
Submodule.restrictScalars_sup
∀ (S : Type u_1) {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Semiring S]
[inst_3 : Module S M] [inst_4 : Module R M] [inst_5 : SMul S R] [inst_6 : IsScalarTower S R M] (s t : Submodule R M),
Submodule.restrictScalars S (s ⊔ t) = Submodule.restrictScalars S s ⊔ Submodule.restrictScalars S t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- SupSet.sSupproof · cited by 954
- Submodule.restrictScalarsstatement and proof · cited by 180
- Set.image_singletonproof · cited by 174
- Set.image_insert_eqproof · cited by 37
- Submodule.restrictScalars.congr_simpproof · cited by 17
- sSup_singletonproof · cited by 14
- sSup_insertproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- PointedCone.ofSubmodule_supproof · cited by 0