Theorems · Theorem · number theory
Nat.find_le
∀ {n : ℕ} {p : ℕ → Prop} [inst : DecidablePred p] {h : ∃ n, p n}, p n → Nat.find h ≤ n- Defined in
- Mathlib.Data.Nat.Find
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_reflproof · cited by 2,061
- Nat.findstatement · cited by 139
- Nat.find_le_iffproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Subgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 5
- AddSubgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_leproof · cited by 5
- AddSubgroup.upperCentralSeries_eq_top_iff_nilpotencyClass_leproof · cited by 4
- Subgroup.lowerCentralSeries_eq_bot_iff_nilpotencyClass_leproof · cited by 4
- Group.rank_leproof · cited by 4
- AddGroup.rank_leproof · cited by 3
- toZ_of_eqproof · cited by 2
- Associates.count_factors_eq_find_of_dvd_powproof · cited by 1
- Nat.find_addproof · cited by 1