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Theorems · Theorem · order theory

WithBot.succ_eq_succ

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : OrderBot α] [inst_2 : SuccOrder α] (a : WithBot α),
  ↑a.succ = Order.succ a
Defined in
Mathlib.Order.SuccPred.WithBot
Cited by
1 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
PreorderOrderBotSuccOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithBot.lt_succ · cited by 0WithBot.lt_succPreorder · cited by 7952PreorderWithBot · cited by 1498WithBotOrderBot · cited by 1055OrderBotOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderWithBot.some · cited by 541WithBot.someWithBot.succ · cited by 30WithBot.succWithBot.succ_eq_succCITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.