Theorems · Theorem · order theory
Order.succ_eq_zero
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : AddZeroClass α] [inst_2 : OrderBot α] [IsBotZeroClass α]
[inst_4 : One α] [NoMaxOrder α] [inst_6 : SuccAddOrder α] {a : WithBot α}, a.succ = 0 ↔ a = ⊥- Defined in
- Mathlib.Algebra.Order.SuccPred
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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.botstatement and proof · cited by 4,720
- WithBotstatement and proof · cited by 1,498
- AddZeroClassstatement and proof · cited by 1,237
- OrderBotstatement and proof · cited by 1,055
- WithBot.someproof · cited by 541
- NoMaxOrderstatement and proof · cited by 340
- Order.succ_eq_add_oneproof · cited by 115
- SuccAddOrderstatement and proof · cited by 108
- WithBot.recBotCoeproof · cited by 101
- IsBotZeroClassstatement and proof · cited by 71
- bot_eq_zeroproof · cited by 31
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