Theorems · Theorem · linear algebra
LinearMap.ker_fst
∀ (R : Type u) (M : Type v) (M₂ : Type w) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂], (LinearMap.fst R M M₂).ker = (LinearMap.inr R M M₂).range
- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- LinearMap.rangestatement · cited by 893
- LinearMap.kerstatement · cited by 848
- LinearMap.fststatement · cited by 64
- LinearMap.inrstatement · cited by 62
- LinearMap.range_inrproof · cited by 3
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