Theorems · Theorem · order theory
CompositionSeries.Equivalent.trans
∀ {X : Type u} [inst : Lattice X] [inst_1 : JordanHolderLattice X] {s₁ s₂ s₃ : CompositionSeries X},
s₁.Equivalent s₂ → s₂.Equivalent s₃ → s₁.Equivalent s₃- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Classical.choice, Quot.sound
- Assumes
- LatticeJordanHolderLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Latticestatement and proof · cited by 916
- Equiv.transproof · cited by 337
- RelSeries.lengthproof · cited by 195
- JordanHolderLatticestatement and proof · cited by 44
- CompositionSeriesstatement and proof · cited by 40
- CompositionSeries.Equivalentstatement and proof · cited by 9
- JordanHolderLattice.iso_transproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CompositionSeries.exists_last_eq_snoc_equivalentproof · cited by 1
- CompositionSeries.jordan_holderproof · cited by 1