Theorems · Theorem · order theory
Set.OrdConnected.apply_wcovBy_apply_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {a b : α} (f : α ↪o β),
(Set.range ⇑f).OrdConnected → (f a ⩿ f b ↔ a ⩿ b)- Defined in
- Mathlib.Order.Cover
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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 and proof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Set.rangestatement and proof · cited by 4,705
- OrderEmbeddingstatement and proof · cited by 619
- Set.OrdConnectedstatement and proof · cited by 161
- WCovBystatement and proof · cited by 107
- WCovBy.imageproof · cited by 2
- WCovBy.of_imageproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Finset.val_wcovBy_valproof · cited by 1
- Finset.coe_wcovBy_coeproof · cited by 1
- apply_wcovBy_apply_iffproof · cited by 1
- WithTop.coe_wcovBy_coeproof · cited by 0
- WithBot.coe_wcovBy_coeproof · cited by 0