Theorems · Theorem · linear algebra
Submodule.disjoint_iff_comap_eq_bot
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{p q : Submodule R M}, Disjoint p q ↔ Submodule.comap p.subtype q = ⊥- Defined in
- Mathlib.Algebra.Module.Submodule.Map
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- Disjointstatement and proof · cited by 2,201
- Submodule.mapproof · cited by 614
- Submodule.subtypestatement and proof · cited by 480
- Submodule.comapstatement · cited by 347
- Subtype.coe_injectiveproof · cited by 205
Cited by3
Results whose statement or proof uses this declaration.
- LieSubmodule.comap_incl_eq_botproof · cited by 2
- ContinuousLinearMap.IsFredholm.of_isInvertible_restrictproof · cited by 1
- LieIdeal.comap_incl_eq_botproof · cited by 0