Theorems · Theorem · order theory
CompositionSeries.eq_snoc_eraseLast
∀ {X : Type u} [inst : Lattice X] [inst_1 : JordanHolderLattice X] {s : CompositionSeries X} (h : 0 < s.length),
s = (RelSeries.eraseLast s).snoc (RelSeries.last s) ⋯- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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.
Cites13
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 and proof · cited by 195
- RelSeries.laststatement and proof · cited by 114
- JordanHolderLatticestatement and proof · cited by 44
- JordanHolderLattice.IsMaximalstatement · cited by 42
- CompositionSeriesstatement and proof · cited by 40
- RelSeries.snocstatement · cited by 24
- RelSeries.eraseLaststatement · cited by 21
- RelSeries.last_memproof · cited by 5
- CompositionSeries.extproof · cited by 3
- CompositionSeries.isMaximal_eraseLast_laststatement · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- CompositionSeries.exists_last_eq_snoc_equivalentproof · cited by 1
- CompositionSeries.snoc_eraseLast_lastproof · cited by 1
- CompositionSeries.jordan_holderproof · cited by 1