have h_inductive (idx : Fin rupHints.size) (acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool) (ih : motive idx.1 acc) :=
  confirmRupHint_preserves_motive fc.1 rupHints idx acc ih
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
c : DefaultClause n
rupHints : Array Nat
p : PosFin n → Bool
pf : p ⊨ f
fc : DefaultFormula n × Bool := f.insertRupUnits c.negate
confirmRupHint_fold_res : Array Assignment × List (Literal (PosFin n)) × Bool × Bool :=
  Array.foldl (confirmRupHint fc.fst.clauses) (fc.fst.assignments, [], false, false) rupHints 0
confirmRupHint_success : confirmRupHint_fold_res.snd.snd.fst = true
motive : Nat → Array Assignment × List (Literal (PosFin n)) × Bool × Bool → Prop :=
  fc.fst.confirmRupHint_fold_entails_hsat_motive
h_base : motive 0 (fc.fst.assignments, [], false, false)
⊢ p ⊨ c
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
c : DefaultClause n
rupHints : Array Nat
p : PosFin n → Bool
pf : p ⊨ f
fc : DefaultFormula n × Bool := f.insertRupUnits c.negate
confirmRupHint_fold_res : Array Assignment × List (Literal (PosFin n)) × Bool × Bool :=
  Array.foldl (confirmRupHint fc.fst.clauses) (fc.fst.assignments, [], false, false) rupHints 0
confirmRupHint_success : confirmRupHint_fold_res.snd.snd.fst = true
motive : Nat → Array Assignment × List (Literal (PosFin n)) × Bool × Bool → Prop :=
  fc.fst.confirmRupHint_fold_entails_hsat_motive
h_base : motive 0 (fc.fst.assignments, [], false, false)
h_inductive :
  ∀ (idx : Fin rupHints.size) (acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool),
    motive (↑idx) acc →
      fc.fst.confirmRupHint_fold_entails_hsat_motive (↑idx + 1) (confirmRupHint fc.fst.clauses acc rupHints[idx])
⊢ p ⊨ c