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Theorems · Theorem · order theory

Order.succ_le_succ_iff

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α],
  Order.succ a ≤ Order.succ b ↔ a ≤ b
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
4 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSuccOrderNoMaxOrder
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Around this declaration

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

Ordinal.blsub_comp · cited by 2Ordinal.blsub_compONote.repr_opow_aux₂ · cited by 1ONote.repr_opow_aux₂Order.le_of_succ_le_succ · cited by 0Order.le_of_succ_le_succCardinal.exists_uncountable_fiber · cited by 0Cardinal.exists_uncountab…LinearOrder · cited by 8572LinearOrderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderNoMaxOrder · cited by 340NoMaxOrderOrder.succ_le_succ_iffCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.