Theorems · Theorem · order theory
WithBot.succ_natCast
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : OrderBot α] [inst_2 : AddMonoidWithOne α] [inst_3 : SuccAddOrder α]
(n : ℕ), (↑n).succ = ↑n + 1- Defined in
- Mathlib.Algebra.Order.SuccPred.WithBot
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- WithBotstatement and proof · cited by 1,498
- OrderBotstatement and proof · cited by 1,055
- AddMonoidWithOnestatement and proof · cited by 313
- Order.succ_eq_add_oneproof · cited by 115
- SuccAddOrderstatement and proof · cited by 108
- WithBot.succstatement and proof · cited by 30
- WithBot.coe_natCastproof · cited by 4
- WithBot.succ_coeproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ChevalleyThm.chevalley_mvPolynomialCproof · cited by 1
- WithBot.succ_ofNatproof · cited by 0
- WithBot.succ_oneproof · cited by 0
- WithBot.succ_zeroproof · cited by 0