Theorems · Theorem · linear algebra
Submodule.quotientRel_def
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M)
{x y : M}, p.quotientRel x y ↔ x - y ∈ p- Defined in
- Mathlib.LinearAlgebra.Quotient.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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
- Submodulestatement and proof · cited by 7,192
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- Submodule.toAddSubgroupproof · cited by 106
- neg_addproof · cited by 69
- neg_mem_iffproof · cited by 42
- QuotientAddGroup.leftRel_applyproof · cited by 20
- Submodule.quotientRelstatement · cited by 18
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.Quotient.eqproof · cited by 21
- LinearMap.FiniteRangeSetoid.equiv_iff_hasNoetherianRangeproof · cited by 5
- ArchimedeanClass.FiniteResidueField.mk_eq_mkproof · cited by 1
- UniformSpace.inseparableSetoid_ringproof · cited by 0