Theorems · Theorem · order theory
Set.Icc_subset_Icc_union_Icc
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α}, Set.Icc a c ⊆ Set.Icc a b ∪ Set.Icc b c- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Iccstatement and proof · cited by 1,702
- Set.Subset.transproof · cited by 218
- Set.Ioc_subset_Icc_selfproof · cited by 53
- Set.union_subset_union_rightproof · cited by 19
- Set.Icc_subset_Icc_union_Iocproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Set.Icc_union_Icc_eq_Iccproof · cited by 5