Theorems · Theorem · logic and foundations

Order.enum_succ_le_of_lt

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] [inst_2 : IsRegularCardinalOrder α] {s : Set α}
  {hs : IsCofinal s} [inst_3 : SuccOrder α] {a o : α},
  o ∈ s → ↑((Order.enum s hs) a) < o → ↑((Order.enum s hs) (Order.succ a)) ≤ o

Defined in

Mathlib.SetTheory.Cardinal.Cofinality.Enum

Cited by

0 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLTIsRegularCardinalOrderSuccOrder