Theorems · Theorem · linear algebra
LinearMap.IsProj.submodule_eq_bot_iff
∀ {S : Type u_5} [inst : Semiring S] {M : Type u_6} [inst_1 : AddCommMonoid M] [inst_2 : Module S M] {m : Submodule S M}
{f : M →ₗ[S] M}, LinearMap.IsProj m f → (m = ⊥ ↔ f = 0)- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- LinearMap.extproof · cited by 844
- LinearMap.IsProjstatement and proof · cited by 23
- LinearMap.range_zeroproof · cited by 11
- LinearMap.IsProj.map_memproof · cited by 3
- LinearMap.IsProj.rangeproof · cited by 3
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