∀ {S : Finset Turing.PartrecToTM2.Λ'} {c : Turing.ToPartrec.Code} {k : Turing.PartrecToTM2.Cont'},
  Turing.PartrecToTM2.codeSupp c k ⊆ S → Turing.PartrecToTM2.Supports (Turing.PartrecToTM2.codeSupp' c k) S