Mathlib Map

Theorems · Theorem · order theory

Order.isPredPrelimit_toDual_iff

∀ {α : Type u_1} {a : α} [inst : LT α], Order.IsPredPrelimit (OrderDual.toDual a) ↔ Order.IsSuccPrelimit a
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
LT
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.IsSuccPrelimit.dual · cited by 2IsSuccPrelimit.dualOrder.isPredLimit_toDual_iff · cited by 1Order.isPredLimit_toDual_…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivOrderDual · cited by 927OrderDualOrderDual.toDual · cited by 481OrderDual.toDualCovBy · cited by 290CovByOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitOrder.IsPredPrelimit · cited by 93Order.IsPredPrelimittoDual_covBy_toDual_iff · cited by 4toDual_covBy_toDual_iffOrderDual.forall · cited by 2OrderDual.forallOrder.isPredPrelimit_toDual_i…CITED 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.