Theorems · Theorem · ring theory
IsIsotypicOfType.of_subsingleton
∀ (R : Type u_2) (M : Type u) (S : Type u_4) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup S] [inst_3 : Module R M] [inst_4 : Module R S] [Subsingleton M], IsIsotypicOfType R M S
- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Nontrivialproof · cited by 2,416
- IsSimpleModuleproof · cited by 114
- Submodule.subtype_injectiveproof · cited by 25
- not_subsingletonproof · cited by 24
- IsIsotypicOfTypestatement · cited by 16
- Function.Injective.subsingletonproof · cited by 16
- IsSimpleModule.nontrivialproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsIsotypic.of_subsingletonproof · cited by 0