Theorems · Theorem · category theory

Profinite.NobelingProof.GoodProducts.maxTail_isGood

∀ {I : Type u} (C : Set (I → Bool)) [inst : LinearOrder I] [inst_1 : WellFoundedLT I] {o : Ordinal.{u}},
  IsClosed C →
    Profinite.NobelingProof.contained C (Order.succ o) →
      ∀ (ho : o < Ordinal.type fun x1 x2 => x1 < x2) (l : ↑(Profinite.NobelingProof.GoodProducts.MaxProducts C ho)),
        ⊤ ≤
            Submodule.span ℤ
              (Set.range
                (Profinite.NobelingProof.GoodProducts.eval
                  (Profinite.NobelingProof.π C fun x => Profinite.NobelingProof.ord I x < o))) →
          Profinite.NobelingProof.Products.isGood (Profinite.NobelingProof.C' C ho) (↑l).Tail

Removing the leading o from a term of MaxProducts C yields a list which isGood with respect to C'.

Defined in

Mathlib.Topology.Category.Profinite.Nobeling.Successor

Cited by

0 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLT