Theorems · Theorem · linear algebra
Submodule.IsCompl.projection_eq_self_sub_projection
Deprecated since 2026-05-05Use Submodule.projection_eq_self_sub_projection instead.
∀ {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}
(hpq : IsCompl p q) (x : E), (q.projection p ⋯) x = x - (p.projection q hpq) xAlias of Submodule.projection_eq_self_sub_projection.
- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites11
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 · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement · cited by 7,463
- Submodulestatement · cited by 7,192
- IsComplstatement · cited by 351
- IsCompl.symmstatement · cited by 80
- Submodule.projectionstatement · cited by 63
- Submodule.projection_eq_self_sub_projectionproof · cited by 4
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