Theorems · Theorem · number theory
Nat.nth_lt_nth
∀ {p : ℕ → Prop}, (Set.ofPred p).Infinite → ∀ {k n : ℕ}, Nat.nth p k < Nat.nth p n ↔ k < n- Defined in
- Mathlib.Data.Nat.Nth
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- Set.Infinitestatement and proof · cited by 263
- StrictMono.lt_iff_ltproof · cited by 86
- Nat.nthstatement · cited by 84
- Nat.nth_strictMonoproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Nat.nth_lt_nth'proof · cited by 4
- Nat.le_nth_of_lt_nth_succproof · cited by 1