Theorems · Theorem · order theory
Finset.Ico_union_Ico_eq_Ico
∀ {α : Type u_2} [inst : LinearOrder α] [inst_1 : LocallyFiniteOrder α] {a b c : α},
a ≤ b → b ≤ c → Finset.Ico a b ∪ Finset.Ico b c = Finset.Ico a c- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coeproof · cited by 8,199
- Set.Icoproof · cited by 799
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement and proof · cited by 450
- Finset.coe_unionproof · cited by 78
- Finset.coe_Icoproof · cited by 66
- Finset.coe_injproof · cited by 41
- Set.Ico_union_Ico_eq_Icoproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Finset.sum_Ico_consecutiveproof · cited by 10
- Finset.range_add_eq_unionproof · cited by 1
- Finset.prod_Ico_consecutiveproof · cited by 1
- Nat.primeCounting'_add_leproof · cited by 1
- primorial_addproof · cited by 1
- Polynomial.aeval_sumIDeriv_of_posproof · cited by 1
- Multiset.Ico_add_Ico_eq_Icoproof · cited by 0