have c_in_f : c ∈ toList f := by
  simp only [toList, Array.toList_eq, List.append_assoc, List.mem_append, List.mem_filterMap, id_eq,
    exists_eq_right, List.mem_map, Prod.exists, Bool.exists_bool]
  apply Or.inl
  simp only [getElem?] at hc
  split at hc
  . simp only [Option.some.injEq] at hc
    rw [← hc]
    apply Array.getElem_mem_data
  . exact False.elim hc
n : Nat
f : DefaultFormula n
rupHints : Array Nat
idx : Fin rupHints.size
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
h1 : limplies (PosFin n) f acc.fst
h2 : acc.snd.snd.fst = true → incompatible (PosFin n) acc.fst f
acc2_eq_false : acc.2.2.snd = false ∧ acc.2.2.fst = false
x✝ : Option (Option (DefaultClause n))
c : DefaultClause n
hc : f.clauses[rupHints[↑idx]]? = some (some c)
⊢ f.confirmRupHint_fold_entails_hsat_motive (↑idx + 1)
    (match c.reduce acc.fst with
    | encounteredBoth => (acc.fst, acc.2.fst, true, false)
    | reducedToEmpty => (acc.fst, acc.2.fst, true, false)
    | reducedToUnit (l, b) =>
      if hasAssignment b acc.fst[l.val]! = true then (acc.fst, acc.2.fst, false, false)
      else (acc.fst.modify l.val (addAssignment b), (l, b) :: acc.2.fst, false, false)
    | reducedToNonunit => (acc.fst, acc.2.fst, false, true))
n : Nat
f : DefaultFormula n
rupHints : Array Nat
idx : Fin rupHints.size
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
h1 : limplies (PosFin n) f acc.fst
h2 : acc.snd.snd.fst = true → incompatible (PosFin n) acc.fst f
acc2_eq_false : acc.2.2.snd = false ∧ acc.2.2.fst = false
x✝ : Option (Option (DefaultClause n))
c : DefaultClause n
hc : f.clauses[rupHints[↑idx]]? = some (some c)
c_in_f : c ∈ f.toList
⊢ f.confirmRupHint_fold_entails_hsat_motive (↑idx + 1)
    (match c.reduce acc.fst with
    | encounteredBoth => (acc.fst, acc.2.fst, true, false)
    | reducedToEmpty => (acc.fst, acc.2.fst, true, false)
    | reducedToUnit (l, b) =>
      if hasAssignment b acc.fst[l.val]! = true then (acc.fst, acc.2.fst, false, false)
      else (acc.fst.modify l.val (addAssignment b), (l, b) :: acc.2.fst, false, false)
    | reducedToNonunit => (acc.fst, acc.2.fst, false, true))