Theorems · Theorem · linear algebra
Submodule.sub_projection_mem
∀ {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 : E), x - (p.projection q h) x ∈ q- 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
Around this declaration
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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
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsComplstatement and proof · cited by 351
- IsCompl.symmproof · cited by 80
- Submodule.projectionstatement · cited by 63
- Submodule.projection_eq_self_sub_projectionproof · cited by 4
- Submodule.projection_apply_memproof · cited by 3
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