Theorems · Theorem · logic and foundations
Cardinal.mk_Iio_lt
∀ {α : Type u} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] (i : α),
((Cardinal.mk α).ord = Ordinal.type fun x1 x2 => x1 < x2) → Cardinal.mk ↑(Set.Iio i) < Cardinal.mk α- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
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.
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Ordinalstatement · cited by 1,688
- Set.Iiostatement · cited by 1,166
- Cardinal.mkstatement and proof · cited by 942
- WellFoundedLTstatement and proof · cited by 491
- Cardinal.ordstatement and proof · cited by 266
- Ordinal.typestatement and proof · cited by 207
- IsWellOrderstatement · cited by 171
- Cardinal.card_typein_ltproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.mul_eq_selfproof · cited by 13
- Cardinal.mk_Iio_toType_ord_ltproof · cited by 2
- Cardinal.mk_Iic_ltproof · cited by 2
- Cardinal.lt_power_cof_ordproof · cited by 2
- Cardinal.mk_Ioi_ltproof · cited by 0
- Cardinal.exists_rel_mk_fibers_ltproof · cited by 0