Theorems · Theorem · number theory
Nat.findGreatest_spec
∀ {m : ℕ} {P : ℕ → Prop} [inst : DecidablePred P] {n : ℕ}, m ≤ n → P m → P (Nat.findGreatest P n)- Defined in
- Mathlib.Data.Nat.Find
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 69 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.findGreateststatement and proof · cited by 25
- Nat.findGreatest_eq_iffproof · cited by 6
- Nat.findGreatest_eq_zero_iffproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- addRothNumber_specproof · cited by 8
- mulRothNumber_specproof · cited by 6
- Nat.fib_greatestFib_leproof · cited by 2
- PairReduction.iSup_edist_pairSetproof · cited by 1
- Primrec.of_graphproof · cited by 1
- LowerHemicontinuousAt.exists_seq_tendstoproof · cited by 1
- exists_frobeniusNumber_iffproof · cited by 0
- ruzsaSzemerediNumber_specproof · cited by 0