Theorems · Theorem · linear algebra
Submodule.factor_surjective
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {p p' : Submodule R M}
(H : p ≤ p'), Function.Surjective ⇑(Submodule.factor H)- Defined in
- Mathlib.LinearAlgebra.Quotient.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Submodule.Quotient.mkproof · cited by 184
- Quotient.outproof · cited by 141
- Quotient.out_eqproof · cited by 27
- Submodule.factorstatement · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.quotOfMul_surjectiveproof · cited by 1
- Ring.ord_le_ord_mulproof · cited by 1
- LinearMap.rank_quot_submodule_map_eqproof · cited by 1
- AdicCompletion.surjective_evalₐproof · cited by 1
- LinearMap.index_compproof · cited by 0