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Theorems · Theorem · order theory

Order.IsSuccLimit.succ_ne

∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : SuccOrder α] [NoMaxOrder α],
  Order.IsSuccLimit a → ∀ (b : α), Order.succ b ≠ a
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderSuccOrderNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.not_isSuccLimit_succ · cited by 2Order.not_isSuccLimit_succPreorder · cited by 7952PreorderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderNoMaxOrder · cited by 340NoMaxOrderOrder.IsSuccLimit · cited by 255Order.IsSuccLimitOrder.IsSuccLimit.isSuccPrelimit · cited by 37IsSuccLimit.isSuccPrelimitOrder.IsSuccPrelimit.succ_ne · cited by 3IsSuccPrelimit.succ_neIsSuccLimit.succ_neCITED 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.