Theorems · Theorem · commutative algebra
Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective
∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.PreSubmersivePresentation R S ι σ) [inst_3 : Finite σ],
IsUnit P.jacobian ↔ Function.Bijective ⇑P.aevalDifferential- Cited by
- 1 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Finitestatement and proof · cited by 3,029
- IsUnitstatement and proof · cited by 1,602
- Function.Bijectivestatement and proof · cited by 863
- Algebra.PreSubmersivePresentationstatement and proof · cited by 54
- Algebra.PreSubmersivePresentation.jacobianstatement · cited by 31
- Module.End.isUnit_iffproof · cited by 21
- Algebra.PreSubmersivePresentation.aevalDifferentialstatement and proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.