Theorems · Theorem · logic and foundations
Nat.Subtype.exists_succ
∀ {s : Set ℕ} [Infinite ↑s] (x : ↑s), ∃ n, ↑x + n + 1 ∈ s- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 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.
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 and proof · cited by 7,166
- lt_of_not_geproof · cited by 374
- Infinitestatement and proof · cited by 352
- Multiset.toFinsetproof · cited by 230
- Multiset.filterproof · cited by 102
- Multiset.rangeproof · cited by 30
- Multiset.pmapproof · cited by 16
- Fintype.falseproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Nat.Subtype.succproof · cited by 6
- Nat.Subtype.succ_le_of_ltproof · cited by 2
- Nat.Subtype.le_succ_of_forall_lt_leproof · cited by 1
- Nat.Subtype.lt_succ_selfproof · cited by 1