Theorems · Theorem · order theory
CompositionSeries.le_last_of_mem
∀ {X : Type u} [inst : Lattice X] [inst_1 : JordanHolderLattice X] {s : CompositionSeries X} {x : X},
x ∈ s → x ≤ RelSeries.last s- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 33 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.
Cites11
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
- RelSeries.lengthproof · cited by 195
- RelSeries.laststatement and proof · cited by 114
- RelSeries.toFunproof · cited by 114
- Set.mem_rangeproof · cited by 102
- JordanHolderLatticestatement and proof · cited by 44
- JordanHolderLattice.IsMaximalstatement · cited by 42
- CompositionSeriesstatement and proof · cited by 40
- CompositionSeries.le_lastproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CompositionSeries.exists_last_eq_snoc_equivalentproof · cited by 1
- CompositionSeries.lt_last_of_mem_eraseLastproof · cited by 0