Theorems · Theorem · order theory
WithBot.succ_zero
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : OrderBot α] [inst_2 : AddMonoidWithOne α] [inst_3 : SuccAddOrder α],
WithBot.succ 0 = 1- Defined in
- Mathlib.Algebra.Order.SuccPred.WithBot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- WithBotstatement · cited by 1,498
- OrderBotstatement and proof · cited by 1,055
- AddMonoidWithOnestatement and proof · cited by 313
- SuccAddOrderstatement and proof · cited by 108
- WithBot.succstatement and proof · cited by 30
- WithBot.succ_natCastproof · cited by 4
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