Theorems · Theorem · order theory
Finpartition.le
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] {a : α} (P : Finpartition a) {b : α}, b ∈ P.parts → b ≤ a- Defined in
- Mathlib.Order.Partition.Finpartition
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- LE.le.transproof · cited by 3,151
- OrderBotstatement and proof · cited by 1,055
- Latticestatement and proof · cited by 916
- Eq.leproof · cited by 605
- Finpartitionstatement and proof · cited by 199
- Finpartition.partsstatement and proof · cited by 184
- Finset.le_supproof · cited by 112
- Finpartition.sup_partsproof · cited by 15
Cited by15
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_leproof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3
- MeasureTheory.IsSetSemiring.notMem_disjointOfDiffproof · cited by 2
- MeasureTheory.VectorMeasure.exists_variation_le_add'proof · cited by 2
- Finpartition.exists_le_of_leproof · cited by 1
- Finpartition.sum_combineproof · cited by 1
- MeasureTheory.VectorMeasure.exists_lt_sum_of_lt_variationproof · cited by 1
- MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnionproof · cited by 1
- Finpartition.part_eq_iff_memproof · cited by 1
- Finpartition.part_surjOnproof · cited by 1
- Finpartition.card_bindproof · cited by 1
- Finpartition.card_extendproof · cited by 0