Theorems · Theorem · order theory
Set.Icc_eq_singleton_iff
∀ {α : Type u_1} [inst : PartialOrder α] {a b c : α}, Set.Icc a b = {c} ↔ a = c ∧ b = c- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrder
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.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccstatement and proof · cited by 1,702
- Set.left_mem_Iccproof · cited by 67
- Set.Icc_selfproof · cited by 63
- Set.right_mem_Iccproof · cited by 60
- Set.singleton_nonemptyproof · cited by 32
- Set.eq_of_mem_singletonproof · cited by 22
- Set.nonempty_Iccproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Finset.Icc_eq_singleton_iffproof · cited by 2