Theorems · Theorem · commutative algebra
Submodule.comap_subtype_eq_top
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{p p' : Submodule R M}, Submodule.comap p.subtype p' = ⊤ ↔ p ≤ p'- Defined in
- Mathlib.Algebra.Module.Submodule.Range
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 66 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.
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Submodule.subtypestatement · cited by 480
- Submodule.comapstatement · cited by 347
- eq_top_iffproof · cited by 236
- Submodule.map_le_iff_le_comapproof · cited by 49
- Submodule.map_subtype_topproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.eq_of_le_of_finrank_leproof · cited by 10
- Submodule.comap_subtype_selfproof · cited by 9
- Module.FaithfullyFlat.rTensor_reflects_exactproof · cited by 2
- LieSubmodule.comap_incl_eq_topproof · cited by 0
- LieIdeal.comap_incl_eq_topproof · cited by 0