Theorems · Theorem · logic and foundations
Nat.Subtype.lt_succ_iff_le
∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s] {x y : ↑s}, x < Nat.Subtype.succ y ↔ x ≤ y- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- InfiniteDecidablePred
Around this declaration
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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_le_of_ltproof · cited by 432
- le_of_not_gtproof · cited by 430
- Infinitestatement and proof · cited by 352
- not_le_of_gtproof · cited by 97
- Nat.Subtype.succstatement and proof · cited by 6
- Nat.Subtype.succ_le_of_ltproof · cited by 2
- Nat.Subtype.lt_succ_selfproof · cited by 1
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