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Theorems · Theorem · order theory

IsCompl.ofDual

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : BoundedOrder α] {a b : αᵒᵈ},
  IsCompl a b → IsCompl (OrderDual.ofDual a) (OrderDual.ofDual b)
Defined in
Mathlib.Order.Disjoint
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses Quot.sound
Assumes
PartialOrderBoundedOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isCompl_ofDual_iff · cited by 0isCompl_ofDual_iffisCompl_toDual_iff · cited by 0isCompl_toDual_iffDFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivPartialOrder · cited by 6410PartialOrderOrderDual · cited by 927OrderDualOrderDual.ofDual · cited by 400OrderDual.ofDualIsCompl · cited by 351IsComplBoundedOrder · cited by 270BoundedOrderIsCompl.disjoint · cited by 42IsCompl.disjointIsCompl.codisjoint · cited by 32IsCompl.codisjointIsCompl.ofDualCITED BYCITES

Cites9

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

Cited by2

Results whose statement or proof uses this declaration.