Theorems · Theorem · order theory

SuccOrder.forall_ne_bot_iff

∀ {α : Type u_1} [Nontrivial α] [inst : PartialOrder α] [inst_1 : OrderBot α] [inst_2 : SuccOrder α]
  [IsSuccArchimedean α] (P : α → Prop), (∀ (i : α), i ≠ ⊥ → P i) ↔ ∀ (i : α), P (SuccOrder.succ i)

Defined in

Mathlib.Order.SuccPred.Archimedean

Cited by

1 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontrivialPartialOrderOrderBotSuccOrderIsSuccArchimedean