Theorems · Theorem · field theory
IsPurelyInseparable.injective_restrictDomain
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [IsPurelyInseparable F E] (R : Type u_1) (L : Type u_2) [inst_4 : CommSemiring R] [inst_5 : Algebra R F] [inst_6 : Algebra R E] [inst_7 : CommRing L] [IsReduced L] [inst_9 : Algebra R L] [inst_10 : IsScalarTower R F E], Function.Injective (AlgHom.domRestrict F)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- RingHomClass.toRingHomproof · cited by 746
- AlgHom.toRingHomproof · cited by 490
- IsReducedstatement and proof · cited by 98
- IsPurelyInseparablestatement and proof · cited by 84
- AlgHom.coe_ringHom_injectiveproof · cited by 20
- AlgHom.domRestrictstatement and proof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.bijective_restrictDomainproof · cited by 0