Theorems · Theorem · logic and foundations

Cardinal.mk_bounded_subset

∀ {α : Type u_1},
  (Cardinal.mk α).IsStrongPrelimit →
    ∀ {r : α → α → Prop} [inst : IsWellOrder α r],
      (Cardinal.mk α).ord = Ordinal.type r → Cardinal.mk { s // Set.Bounded r s } = Cardinal.mk α

Defined in: Mathlib.SetTheory.Cardinal.Cofinality.Ordinal
Cited by: 1 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: IsWellOrder

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Cites42

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setstatement and proof · cited by 53,352
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
LE.le.transproof · cited by 3,151
Cardinalstatement and proof · cited by 2,598
Set.iUnionproof · cited by 2,483
LT.lt.leproof · cited by 2,189
le_antisymmproof · cited by 2,068
le_reflproof · cited by 2,061
Ordinalstatement and proof · cited by 1,688
eq_or_neproof · cited by 1,117

Cited by1

Results whose statement or proof uses this declaration.

Cardinal.mk_subset_mk_lt_cofproof · cited by 0