Theorems · Theorem · order theory
Finset.Icc_eq_cons_Ico
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrder α] {a b : α},
a ≤ b → Finset.Icc a b = Finset.cons b (Finset.Ico a b) ⋯Finset.cons version of Finset.Ico_insert_right.
- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, 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.
- Finsetstatement and proof · cited by 13,712
- PartialOrderstatement and proof · cited by 6,410
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement and proof · cited by 450
- Finset.Iccstatement and proof · cited by 348
- Finset.consstatement · cited by 221
- Finset.cons_eq_insertproof · cited by 59
- Finset.right_notMem_Icostatement and proof · cited by 13
- Finset.Ico_insert_rightproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Finset.card_Ico_eq_card_Icc_sub_oneproof · cited by 8
- Commute.add_pow_prime_pow_eq'proof · cited by 3
- Finset.prod_Icc_eq_prod_Ico_mulproof · cited by 1
- Finset.mul_prod_Ico_eq_prod_Iccproof · cited by 1
- Finset.sum_Icc_eq_sum_Ico_addproof · cited by 1
- Finset.add_sum_Ico_eq_sum_Iccproof · cited by 1
- IncidenceAlgebra.sum_Icc_mu_rightproof · cited by 1