Theorems · Theorem · functional analysis
Submodule.projectionOntoL_apply_left
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : TopologicalSpace M] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] {p q : Submodule R M} (h : Submodule.IsTopCompl p q) (x : ↥p), (p.projectionOntoL q h) ↑x = x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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
- TopologicalSpacestatement and proof · cited by 24,529
- 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
- ContinuousLinearMapstatement · cited by 5,352
- Submodule.IsTopComplstatement and proof · cited by 89
- Submodule.IsTopCompl.isComplproof · cited by 44
- Submodule.projectionOnto_apply_leftproof · cited by 23
- Submodule.projectionOntoLstatement · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.IsTopCompl.closedComplementedproof · cited by 8
- Submodule.isQuotientMap_projectionOntoLproof · cited by 1
- ContinuousLinearMap.FredholmPackage.equiv_eq_restrictproof · cited by 1