Theorems · Theorem · order theory
CompositionSeries.lt_last_of_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- Defined in
- Mathlib.Order.JordanHolder
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LatticeJordanHolderLattice
Around this declaration
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Cites12
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
- lt_of_le_of_neproof · cited by 230
- RelSeries.lengthstatement and proof · cited by 195
- RelSeriesstatement · cited by 129
- RelSeries.laststatement · cited by 114
- JordanHolderLatticestatement and proof · cited by 44
- JordanHolderLattice.IsMaximalstatement · cited by 42
- CompositionSeriesstatement and proof · cited by 40
- RelSeries.eraseLaststatement and proof · cited by 21
- CompositionSeries.le_last_of_memproof · cited by 2
- CompositionSeries.mem_eraseLastproof · cited by 2
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