Theorems · Theorem · order theory
Set.Icc_inter_Icc_eq_singleton
∀ {α : Type u_1} [inst : PartialOrder α] {a b c : α}, a ≤ b → b ≤ c → Set.Icc a b ∩ Set.Icc b c = {b}- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrder
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccstatement and proof · cited by 1,702
- Set.Iicproof · cited by 1,111
- Set.Iciproof · cited by 1,070
- Set.Icc_selfproof · cited by 63
- Set.Ici_inter_Iicproof · cited by 12
- Set.Iic_inter_Iciproof · cited by 6
- Set.inter_singleton_of_memproof · cited by 5
- Set.inter_inter_inter_commproof · cited by 2
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