apply Exists.intro insertRupUnits_assignments_size
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
insertRupUnits_assignments_size : (f.insertRupUnits units).fst.assignments.size = n
⊢ f.clear_insert_induction_motive ⋯ (f.insertRupUnits units).fst.rupUnits 0 (f.insertRupUnits units).fst.assignments
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
insertRupUnits_assignments_size : (f.insertRupUnits units).fst.assignments.size = n
⊢ ∀ (i : Fin n),
    let_fun i_lt_assignments_size := ⋯;
    let_fun i_lt_f_assignments_size := ⋯;
    let assignments_i := (f.insertRupUnits units).fst.assignments[↑i];
    let fassignments_i := f.assignments[↑i];
    (assignments_i = fassignments_i ∧
        ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size),
          ↑j ≥ 0 → (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑i) ∨
      (∃ j b i_gt_zero,
          ↑j ≥ 0 ∧
            (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑i, ⋯⟩, b) ∧
              assignments_i = addAssignment b fassignments_i ∧
                ¬hasAssignment b fassignments_i = true ∧
                  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                    ↑k ≥ 0 → k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑i) ∨
        ∃ j1 j2 i_gt_zero,
          ↑j1 ≥ 0 ∧
            ↑j2 ≥ 0 ∧
              (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑i, ⋯⟩, true) ∧
                (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑i, ⋯⟩, false) ∧
                  assignments_i = both ∧
                    fassignments_i = unassigned ∧
                      ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
                        ↑k ≥ 0 → k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑i