Theorems · Theorem · order theory
Nat.exists_not_and_succ_of_not_zero_of_exists
∀ {p : ℕ → Prop}, ¬p 0 → (∃ n, p n) → ∃ n, ¬p n ∧ p (n + 1)- Defined in
- Mathlib.Data.Nat.Order.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.ne'proof · cited by 1,417
- Nat.findproof · cited by 139
- Nat.find_specproof · cited by 74
- Nat.find_minproof · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- IsSl2Triple.HasPrimitiveVectorWith.exists_natproof · cited by 2
- IsSl2Triple.exists_hasPrimitiveVectorWithproof · cited by 0