Theorems · Theorem · order theory
Finset.card_Ioo_eq_card_Ico_sub_one
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrder α] (a b : α),
(Finset.Ioo a b).card = (Finset.Ico a b).card - 1- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- PartialOrderstatement and proof · cited by 6,410
- Finset.cardstatement and proof · cited by 2,327
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement and proof · cited by 450
- Finset.Ioostatement and proof · cited by 185
- Finset.card_emptyproof · cited by 20
- Finset.card_consproof · cited by 16
- Finset.left_notMem_Iooproof · cited by 6
- Finset.Ico_eq_emptyproof · cited by 5
- Finset.Ico_eq_cons_Iooproof · cited by 4
- Finset.Ioo_eq_emptyproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Finset.card_Ioo_eq_card_Icc_sub_twoproof · cited by 6
- Finset.card_Ioo_eq_card_Ioc_sub_oneproof · cited by 0
- Multiset.card_Ioo_eq_card_Ico_sub_oneproof · cited by 0