Theorems · Theorem · logic and foundations
Nat.Subtype.succ_le_of_lt
∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s] {x y : ↑s}, y < x → Nat.Subtype.succ y ≤ x- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 2 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.
Cites7
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.find_min'proof · cited by 28
- Nat.Subtype.succstatement and proof · cited by 6
- Nat.Subtype.exists_succproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Nat.Subtype.ofNat_surjectiveproof · cited by 1
- Nat.Subtype.lt_succ_iff_leproof · cited by 0