Theorems · Theorem · commutative algebra
Algebra.IsStandardSmoothOfRelativeDimension.trans
∀ (n m : ℕ) (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (T : Type u_1) [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] [Algebra.IsStandardSmoothOfRelativeDimension n R S] [Algebra.IsStandardSmoothOfRelativeDimension m S T], Algebra.IsStandardSmoothOfRelativeDimension (m + n) R T
- Defined in
- Mathlib.RingTheory.Smooth.StandardSmooth
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- IsScalarTowerstatement and proof · cited by 3,896
- Finiteproof · cited by 3,029
- Algebra.PreSubmersivePresentation.toPresentationproof · cited by 84
- Algebra.SubmersivePresentationproof · cited by 52
- Algebra.SubmersivePresentation.toPreSubmersivePresentationproof · cited by 47
- Algebra.IsStandardSmoothOfRelativeDimensionstatement and proof · cited by 17
- Algebra.Presentation.dimensionproof · cited by 16
- Algebra.IsStandardSmoothOfRelativeDimension.casesOnproof · cited by 3
- Algebra.SubmersivePresentation.compproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- RingHom.IsStandardSmoothOfRelativeDimension.compproof · cited by 2