Theorems · Theorem · order theory
Set.infinite_of_finite_compl
∀ {α : Type u} [Infinite α] {s : Set α}, sᶜ.Finite → s.Infinite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Compl.complstatement and proof · cited by 2,925
- Set.Finitestatement and proof · cited by 1,814
- Infinitestatement and proof · cited by 352
- Set.Infinitestatement · cited by 263
- Set.Finite.unionproof · cited by 74
- Set.infinite_univproof · cited by 13
- Set.compl_union_selfproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- FirstOrder.Field.ACF_zero_realize_iff_infinite_ACF_prime_realizeproof · cited by 2
- FirstOrder.Field.ACF_zero_realize_iff_finite_ACF_prime_not_realizeproof · cited by 0