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Theorems · Theorem · order theory

Finpartition.extend_parts

∀ {α : Type u_1} [inst : Lattice α] [inst_1 : OrderBot α] [inst_2 : IsModularLattice α] [inst_3 : DecidableEq α]
  {a b c : α} (P : Finpartition a) (hb : b ≠ ⊥) (hab : Disjoint a b) (hc : a ⊔ b = c),
  (P.extend hb hab hc).parts = insert b P.parts
Defined in
Mathlib.Order.Partition.Finpartition
Cited by
3 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LatticeOrderBotIsModularLatticeDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Finpartition.equitabilise_aux · cited by 3Finpartition.equitabilise…MeasureTheory.IsSetSemiring.mem_supClosure_iff · cited by 2IsSetSemiring.mem_supClos…Finpartition.parts_extendOfLE_of_lt · cited by 1Finpartition.parts_extend…Finset · cited by 13712FinsetBot.bot · cited by 4720Bot.botDisjoint · cited by 2201DisjointOrderBot · cited by 1055OrderBotLattice · cited by 916LatticeFinpartition · cited by 199FinpartitionFinpartition.parts · cited by 184Finpartition.partsIsModularLattice · cited by 86IsModularLatticeFinpartition.extend · cited by 5Finpartition.extendFinpartition.extend_partsCITED BYCITES

Cites9

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Cited by3

Results whose statement or proof uses this declaration.