Theorems · Theorem · linear algebra
Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero
∀ {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}, ((p.prodEquivOfIsCompl q h).symm x).2 = 0 ↔ x ∈ p- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- LinearEquiv.symmstatement and proof · cited by 1,461
- IsComplstatement and proof · cited by 351
- LinearEquiv.apply_symm_applyproof · cited by 108
- IsCompl.disjointproof · cited by 42
- Submodule.prodEquivOfIsComplstatement and proof · cited by 35
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