Theorems · Theorem · order theory
Set.Finite.induction_to_univ
∀ {α : Type u} [Finite α] {C : Set α → Prop} (S0 : Set α),
C S0 → (∀ (S : Set α), S ≠ Set.univ → C S → ∃ a ∉ S, C (insert a S)) → C Set.univInduction up to univ.
- Defined in
- Mathlib.Data.Set.Finite.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites6
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.univstatement and proof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- Set.subset_univproof · cited by 228
- Set.finite_univproof · cited by 52
- Set.Finite.induction_toproof · cited by 1
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