Theorems · Theorem · logic and foundations
Cardinal.mk_Iio_toType_ord_lt
Deprecated since 2026-04-12Use Cardinal.mk_Iio_lt instead.
∀ {c : Cardinal.{u_1}} (i : c.ord.ToType), Cardinal.mk ↑(Set.Iio i) < c- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Set.Iiostatement and proof · cited by 1,166
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.ordstatement and proof · cited by 266
- Ordinal.ToTypestatement and proof · cited by 143
- Ordinal.type_toTypeproof · cited by 28
- Cardinal.card_ordproof · cited by 23
- Cardinal.mk_toTypeproof · cited by 12
- Cardinal.mk_Iio_ltproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.card_typein_toType_ltproof · cited by 0
- Cardinal.mk_Iio_ord_toTypeproof · cited by 0