Theorems · Theorem · linear algebra
Submodule.mkQ_apply
∀ {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 : M), p.mkQ x = Submodule.Quotient.mk x- Defined in
- Mathlib.LinearAlgebra.Quotient.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 85 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.
Cites10
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 · cited by 2,301
- Submodule.mkQstatement · cited by 232
- Submodule.Quotient.mkstatement · cited by 184
Cited by21
Results whose statement or proof uses this declaration.
- Submodule.exists_dual_map_eq_bot_of_notMemproof · cited by 4
- IsAdicComplete.mk_liftproof · cited by 2
- IsAdicComplete.StrictMono.mk_liftproof · cited by 2
- Subspace.dualAnnihilator_dualCoannihilator_eqproof · cited by 2
- KaehlerDifferential.kerTotal_mkQ_single_algebraMapproof · cited by 2
- AdicCompletion.of_surjective_iffproof · cited by 2
- exists_linearIndepOn_of_lt_rankproof · cited by 1
- Ideal.finrank_quotient_mapproof · cited by 1
- AdicCompletion.mk_surjectiveproof · cited by 1
- AdicCompletion.mk_zero_ofproof · cited by 1
- Ideal.Quotient.span_singleton_oneproof · cited by 1
- Module.Relations.toQuotient_relationproof · cited by 1