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Theorems · Theorem · order theory

WithBot.succ_coe

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : OrderBot α] [inst_2 : SuccOrder α] (a : α), (↑a).succ = Order.succ a

Not to be confused with WithBot.orderSucc_coe, which is about Order.succ.

Defined in
Mathlib.Order.SuccPred.WithBot
Cited by
2 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
PreorderOrderBotSuccOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.withBotSucc_degree_eq_natDegree_add_one · cited by 6Polynomial.withBotSucc_de…WithBot.succ_natCast · cited by 4WithBot.succ_natCastPreorder · cited by 7952PreorderOrderBot · cited by 1055OrderBotOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderWithBot.some · cited by 541WithBot.someWithBot.succ · cited by 30WithBot.succWithBot.succ_coeCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.