Theorems · Theorem · combinatorics
Set.not_infinite
∀ {α : Type u} {s : Set α}, ¬s.Infinite ↔ s.Finite- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Finitestatement · cited by 1,814
- Set.Infinitestatement · cited by 263
Cited by7
Results whose statement or proof uses this declaration.
- infinite_not_isOfFinAddOrderproof · cited by 2
- hasFiniteSupport_of_finsum_ne_zeroproof · cited by 2
- Set.Finite.not_infiniteproof · cited by 2
- MeasureTheory.Conservative.frequently_measure_inter_ne_zeroproof · cited by 1
- ProbabilityTheory.uniformOn_eq_zero_iffproof · cited by 1
- hasFiniteMulSupport_of_finprod_ne_oneproof · cited by 1
- AddRightCancelMonoid.infinite_not_isOfFinAddOrderproof · cited by 0