Theorems · Theorem · order theory
Nat.WithBot.one_le_iff_zero_lt
∀ {x : WithBot ℕ}, 1 ≤ x ↔ 0 < x- Defined in
- Mathlib.Data.Nat.WithBot
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- zero_addproof · cited by 2,366
- WithBotstatement and proof · cited by 1,498
- LT.lt.trans_leproof · cited by 678
- zero_lt_oneproof · cited by 598
- WithBot.someproof · cited by 541
- WithBot.recBotCoeproof · cited by 101
- WithBot.coe_le_coeproof · cited by 76
- WithBot.coe_lt_coeproof · cited by 55
- not_lt_botproof · cited by 19
- WithBot.coe_zeroproof · cited by 10
- WithBot.coe_oneproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_divByMonic_X_sub_Cproof · cited by 0
- Nat.WithBot.lt_one_iff_le_zeroproof · cited by 0