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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
Assumes
LatticeOrderBot

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_le · cited by 3VectorMeasure.variation_a…Finpartition.equitabilise_aux · cited by 3Finpartition.equitabilise…MeasureTheory.IsSetSemiring.notMem_disjointOfDiff · cited by 2IsSetSemiring.notMem_disj…MeasureTheory.VectorMeasure.exists_variation_le_add' · cited by 2VectorMeasure.exists_vari…Finpartition.exists_le_of_le · cited by 1Finpartition.exists_le_of…Finpartition.sum_combine · cited by 1Finpartition.sum_combineMeasureTheory.VectorMeasure.exists_lt_sum_of_lt_variation · cited by 1VectorMeasure.exists_lt_s…MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion · cited by 1IsSetSemiring.pairwiseDis…Finpartition.part_eq_iff_mem · cited by 1Finpartition.part_eq_iff_…Finpartition.part_surjOn · cited by 1Finpartition.part_surjOnFinpartition.card_bind · cited by 1Finpartition.card_bindFinpartition.card_extend · cited by 0Finpartition.card_extendFinpartition.part_subset · cited by 0Finpartition.part_subsetMeasureTheory.preVariation.iUnion · cited by 0preVariation.iUnionFinpartition.subset · cited by 0Finpartition.subsetFinset · cited by 13712FinsetLE.le.trans · cited by 3151le.transOrderBot · cited by 1055OrderBotLattice · cited by 916LatticeEq.le · cited by 605Eq.leFinpartition · cited by 199FinpartitionFinpartition.parts · cited by 184Finpartition.partsFinset.le_sup · cited by 112Finset.le_supFinpartition.sup_parts · cited by 15Finpartition.sup_partsFinpartition.leCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.