Theorems · Theorem · number theory
Nat.find_eq_zero
∀ {p : ℕ → Prop} [inst : DecidablePred p] (h : ∃ n, p n), Nat.find h = 0 ↔ p 0- Defined in
- Mathlib.Data.Nat.Find
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.findstatement · cited by 139
Cited by6
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_ne_zeroproof · cited by 4
- Nat.find_posproof · cited by 3
- AddGroup.nilpotencyClass_zero_iff_subsingletonproof · cited by 2
- Group.nilpotencyClass_zero_iff_subsingletonproof · cited by 2
- IsPurelyInseparable.elemExponent_eq_zero_of_mem_rangeproof · cited by 1
- Stream'.Seq.length_nilproof · cited by 1