Theorems · Theorem · order theory
Finset.card_Iio_eq_card_Iic_sub_one
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrderBot α] (a : α),
(Finset.Iio a).card = (Finset.Iic a).card - 1- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 3 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.
- Finsetproof · cited by 13,712
- PartialOrderstatement and proof · cited by 6,410
- Finset.cardstatement and proof · cited by 2,327
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicstatement · cited by 280
- Finset.Iiostatement and proof · cited by 147
- Finset.card_consproof · cited by 16
- Finset.notMem_Iio_selfproof · cited by 6
- Finset.Iic_eq_cons_Iioproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Pi.card_Iioproof · cited by 0
- DFinsupp.card_Iioproof · cited by 0
- Finsupp.card_Iioproof · cited by 0