Theorems · Theorem · linear algebra
Submodule.quotientEquivOfIsCompl_apply_mk_right
∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {p q : Submodule R E}
(h : IsCompl p q) (x : ↥q), (p.quotientEquivOfIsCompl q h) (Submodule.Quotient.mk ↑x) = x- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 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
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- LinearEquivstatement · cited by 3,317
- HasQuotient.Quotientstatement · cited by 2,301
- IsComplstatement and proof · cited by 351
- Submodule.Quotient.mkstatement · cited by 184
- LinearEquiv.apply_symm_applyproof · cited by 108
- Submodule.quotientEquivOfIsComplstatement and proof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.quotientEquivOrthogonal_mkproof · cited by 1
- Submodule.quotientEquivOfIsCompl_apply_mk_coeproof · cited by 0