Theorems · Theorem · logic and foundations

Order.enum_le_of_forall_lt

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

Defined in

Mathlib.SetTheory.Cardinal.Cofinality.Enum

Cited by

3 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLTIsRegularCardinalOrder