Theorems · Theorem · linear algebra
LinearMap.le_eqLocus
∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_3} {M₂ : Type u_4} [inst : Semiring R] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
{f g : M →ₛₗ[τ₁₂] M₂} {S : Submodule R M}, S ≤ f.eqLocus g ↔ Set.EqOn ⇑f ⇑g ↑S- Defined in
- Mathlib.Algebra.Module.Submodule.EqLocus
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- SetLike.coestatement · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.EqOnstatement · cited by 603
- LinearMap.eqLocusstatement · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.eqOn_span_iffproof · cited by 1
- LinearMap.eqOn_supproof · cited by 1
- LinearMap.FiniteRangeSetoid.equiv_of_eqOn_coFGproof · cited by 0
- LinearMap.FiniteRangeSetoid.equiv_of_eqOn_of_isNoetherianproof · cited by 0