Theorems · Theorem · order theory
WithBot.one_le_iff_pos
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : AddMonoidWithOne α] [ZeroLEOneClass α] [NeZero 1] [SuccAddOrder α]
(a : WithBot α), 1 ≤ a ↔ 0 < a- Defined in
- Mathlib.Algebra.Order.SuccPred.WithBot
- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botproof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- WithBot.someproof · cited by 541
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- SuccAddOrderstatement and proof · cited by 108
- WithBot.recBotCoeproof · cited by 101
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Splits.degree_eq_one_of_irreducibleproof · cited by 5
- Order.krullDim_eq_one_iff_of_boundedOrderproof · cited by 2