Theorems · Theorem · logic and foundations
WellFounded.cardinalMk_subtype_lt_min_compl_le
∀ {α : Type u} {r : α → α → Prop} (wf : WellFounded r) {s : Set α} (hs : sᶜ.Nonempty),
Cardinal.mk { x // r x (wf.min sᶜ hs) } ≤ Cardinal.mk ↑sThe cardinality of a set is an upper-bound for the amount of elements before the set's mex (minimum excluded value)
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Compl.complstatement and proof · cited by 2,925
- Set.Nonemptystatement and proof · cited by 2,627
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.mk_le_mk_of_subsetproof · cited by 37
- WellFounded.minstatement · cited by 33
- WellFounded.mem_of_lt_min_complproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.card_typein_min_le_mkproof · cited by 1