Theorems · Theorem · logic and foundations
Nat.Subtype.lt_succ_self
∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s] (x : ↑s), x < Nat.Subtype.succ x- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- InfiniteDecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Elemstatement and proof · cited by 7,166
- Infinitestatement and proof · cited by 352
- Nat.findproof · cited by 139
- Nat.Subtype.succstatement · cited by 6
- Nat.Subtype.exists_succproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Subtype.lt_succ_iff_leproof · cited by 0