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Theorems · Theorem · order theory

disjoint_sup_right

∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : OrderBot α] {a b c : α},
  Disjoint a (b ⊔ c) ↔ Disjoint a b ∧ Disjoint a c
Defined in
Mathlib.Order.Disjoint
Cited by
4 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
DistribLatticeOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.disjoint_union_right · cited by 4Set.disjoint_union_rightDisjoint.sup_right · cited by 1Disjoint.sup_rightdisjoint_partialSups_right · cited by 0disjoint_partialSups_rightMultiset.disjoint_union_right · cited by 0Multiset.disjoint_union_r…Bot.bot · cited by 4720Bot.botDisjoint · cited by 2201DisjointOrderBot · cited by 1055OrderBotDistribLattice · cited by 150DistribLatticeinf_sup_left · cited by 28inf_sup_leftdisjoint_sup_rightCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.