Theorems · Theorem · order theory
CompositionSeries.head_le_of_mem
∀ {X : Type u} [inst : Lattice X] [inst_1 : JordanHolderLattice X] {s : CompositionSeries X} {x : X},
x ∈ s → RelSeries.head s ≤ x- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 1 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.toFunproof · cited by 114
- Set.mem_rangeproof · cited by 102
- RelSeries.headstatement and proof · cited by 89
- JordanHolderLatticestatement and proof · cited by 44
- JordanHolderLattice.IsMaximalstatement · cited by 42
- CompositionSeriesstatement and proof · cited by 40
- CompositionSeries.head_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CompositionSeries.jordan_holderproof · cited by 1