Theorems · Theorem · order theory
CompositionSeries.length_pos_of_head_eq_head_of_last_eq_last_of_length_pos
∀ {X : Type u} [inst : Lattice X] [inst_1 : JordanHolderLattice X] {s₁ s₂ : CompositionSeries X},
RelSeries.head s₁ = RelSeries.head s₂ → RelSeries.last s₁ = RelSeries.last s₂ → 0 < s₁.length → 0 < s₂.length- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LatticeJordanHolderLattice
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.
- Set.ofPredstatement · cited by 6,101
- Latticestatement and proof · cited by 916
- RelSeries.lengthstatement · cited by 195
- RelSeries.laststatement and proof · cited by 114
- RelSeries.headstatement and proof · cited by 89
- not_imp_notproof · cited by 63
- JordanHolderLatticestatement and proof · cited by 44
- JordanHolderLattice.IsMaximalstatement · cited by 42
- CompositionSeriesstatement and proof · cited by 40
Cited by1
Results whose statement or proof uses this declaration.
- CompositionSeries.jordan_holderproof · cited by 1