Theorems · Theorem · linear algebra
Submodule.mkQ_map_self
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M),
Submodule.map p.mkQ p = ⊥- Defined in
- Mathlib.LinearAlgebra.Quotient.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 86 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.
Cites14
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
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement · cited by 4,720
- HasQuotient.Quotientstatement · cited by 2,301
- le_reflproof · cited by 2,061
- Submodule.mapstatement · cited by 614
- Submodule.mkQstatement and proof · cited by 232
- eq_bot_iffproof · cited by 159
- Submodule.ker_mkQproof · cited by 63
Cited by8
Results whose statement or proof uses this declaration.
- Submodule.ker_liftQ_eq_botproof · cited by 8
- Submodule.exists_dual_map_eq_bot_of_notMemproof · cited by 4
- ContinuousLinearMap.isStrictMap_isClosed_range_iff_restrictproof · cited by 2
- Ideal.mulQuot_injectiveproof · cited by 1
- Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_supproof · cited by 1
- Ring.jacobson_quotient_jacobsonproof · cited by 0
- LinearMap.index_compproof · cited by 0
- Module.jacobson_quotient_jacobsonproof · cited by 0