∀ {S : Finset Turing.PartrecToTM2.Λ'} {q : Turing.PartrecToTM2.Λ'} {K : Finset Turing.PartrecToTM2.Λ'},
  Turing.PartrecToTM2.Λ'.Supports S q →
    Turing.PartrecToTM2.trStmts₁ q ∪ K ⊆ S →
      (K ⊆ S → Turing.PartrecToTM2.Supports K S) → Turing.PartrecToTM2.Supports (Turing.PartrecToTM2.trStmts₁ q ∪ K) S