{P : Type u_1} →
  {L : Type u_2} →
    {inst : Membership P L} →
      {P_1 : Sort u} →
        {toNondegenerate : Configuration.Nondegenerate P L} →
          {mkLine : {p₁ p₂ : P} → p₁ ≠ p₂ → L} →
            {mkLine_ax : ∀ {p₁ p₂ : P} (h : p₁ ≠ p₂), p₁ ∈ mkLine h ∧ p₂ ∈ mkLine h} →
              {toNondegenerate' : Configuration.Nondegenerate P L} →
                {mkLine' : {p₁ p₂ : P} → p₁ ≠ p₂ → L} →
                  {mkLine_ax' : ∀ {p₁ p₂ : P} (h : p₁ ≠ p₂), p₁ ∈ mkLine' h ∧ p₂ ∈ mkLine' h} →
                    { toNondegenerate := toNondegenerate, mkLine := mkLine, mkLine_ax := mkLine_ax } =
                        { toNondegenerate := toNondegenerate', mkLine := mkLine', mkLine_ax := mkLine_ax' } →
                      (mkLine ≍ mkLine' → P_1) → P_1