Theorems · Theorem · order theory
Part.eq_of_chain
∀ {α : Type u_2} {c : OmegaCompletePartialOrder.Chain (Part α)} {a b : α}, Part.some a ∈ c → Part.some b ∈ c → a = b- Defined in
- Mathlib.Order.OmegaCompletePartialOrder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Partstatement and proof · cited by 325
- le_totalproof · cited by 294
- Part.somestatement and proof · cited by 111
- OmegaCompletePartialOrder.Chainstatement and proof · cited by 85
- OrderHom.monotoneproof · cited by 70
- Part.mem_uniqueproof · cited by 18
- Part.eq_some_iffproof · cited by 17
- OmegaCompletePartialOrder.Chain.toOrderHomproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Part.ωSup_eq_someproof · cited by 0
- Part.mem_ωSupproof · cited by 0