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Theorems · Theorem · order theory

OrderIso.isCoatomic_iff

∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : OrderTop α]
  [inst_3 : OrderTop β] (f : α ≃o β), IsCoatomic α ↔ IsCoatomic β
Defined in
Mathlib.Order.Atoms
Cited by
1 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderPartialOrderOrderTopOrderTop
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Around this declaration

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

CompleteLattice.coatomic_of_top_compact · cited by 0CompleteLattice.coatomic_…PartialOrder · cited by 6410PartialOrderOrderDual · cited by 927OrderDualOrderIso · cited by 874OrderIsoOrderTop · cited by 493OrderTopOrderIso.dual · cited by 24OrderIso.dualIsCoatomic · cited by 23IsCoatomicIsAtomic · cited by 20IsAtomicOrderIso.isAtomic_iff · cited by 1OrderIso.isAtomic_iffOrderIso.isCoatomic_iffCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.