Theorems · Theorem · order theory
InitialSeg.apply_covBy_apply_iff
∀ {α : Type u_1} {β : Type u_2} {a b : α} [inst : PartialOrder α] [inst_1 : PartialOrder β] (f : α ≤i β),
f a ⋖ f b ↔ a ⋖ b- Defined in
- Mathlib.Order.SuccPred.InitialSeg
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- CovBystatement · cited by 290
- InitialSegstatement and proof · cited by 70
- Set.OrdConnected.apply_covBy_apply_iffproof · cited by 8
- InitialSeg.toOrderEmbeddingproof · cited by 8
- IsLowerSet.ordConnectedproof · cited by 5
- InitialSeg.isLowerSet_rangeproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- InitialSeg.isSuccPrelimit_apply_iffproof · cited by 3
- InitialSeg.map_predproof · cited by 1
- InitialSeg.map_succproof · cited by 1
- PrincipalSeg.apply_covBy_apply_iffproof · cited by 0