Theorems · Theorem · order theory
CompositionSeries.mem_eraseLast
∀ {X : Type u} [inst : Lattice X] [inst_1 : JordanHolderLattice X] {s : CompositionSeries X} {x : X},
0 < s.length → (x ∈ RelSeries.eraseLast s ↔ x ≠ RelSeries.last s ∧ x ∈ s)- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 51 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
- Set.rangeproof · cited by 4,705
- Latticestatement and proof · cited by 916
- ne_of_ltproof · cited by 203
- RelSeries.lengthstatement and proof · cited by 195
- RelSeriesstatement · cited by 129
- RelSeries.laststatement and proof · cited by 114
- RelSeries.toFunproof · cited by 114
- JordanHolderLatticestatement and proof · cited by 44
- JordanHolderLattice.IsMaximalstatement · cited by 42
- CompositionSeriesstatement and proof · cited by 40
- RelSeries.eraseLaststatement · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- CompositionSeries.eq_snoc_eraseLastproof · cited by 3
- CompositionSeries.lt_last_of_mem_eraseLastproof · cited by 0