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Theorems · Theorem · order theory

Finset.forall_disjSups_iff

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : SemilatticeSup α] [inst_2 : OrderBot α]
  [inst_3 : DecidableRel Disjoint] {s t : Finset α} {p : α → Prop},
  (∀ c ∈ s.disjSups t, p c) ↔ ∀ a ∈ s, ∀ b ∈ t, Disjoint a b → p (a ⊔ b)
Defined in
Mathlib.Data.Finset.Sups
Cited by
1 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqSemilatticeSupOrderBotDecidableRel
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Around this declaration

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

Finset.disjSups_subset_iff · cited by 0Finset.disjSups_subset_iffFinset · cited by 13712FinsetDisjoint · cited by 2201DisjointOrderBot · cited by 1055OrderBotSemilatticeSup · cited by 785SemilatticeSupFinset.disjSups · cited by 22Finset.disjSupsFinset.forall_disjSups_iffCITED BYCITES

Cites5

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Cited by1

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