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Theorems · Theorem · order theory

Order.succ_lt_succ

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α],
  a < b → Order.succ a < Order.succ b
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderSuccOrderNoMaxOrder
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Around this declaration

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

Order.succ_strictMono · cited by 2Order.succ_strictMonoWithBot.succ_strictMono · cited by 1WithBot.succ_strictMonoPreorder · cited by 7952PreorderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderNoMaxOrder · cited by 340NoMaxOrderOrder.succ_lt_succCITED BYCITES

Cites4

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.