have insertUnit_fold_satisfies_invariant := insertUnit_fold_preserves_invariant f.assignments hf.2.1 f.ratUnits
  f.assignments hf.2.1 false (negate c) h0
case intro
n : Nat
f : DefaultFormula n
hf : f.ratUnits = #[] ∧ f.assignments_invariant
c : DefaultClause n
p : PosFin n → Bool
pf : p ⊨ f
insertUnit_fold_success : (List.foldl insertUnit (f.ratUnits, f.assignments, false) c.negate).2.snd = true
i : PosFin n
hboth : (List.foldl insertUnit (f.ratUnits, f.assignments, false) c.negate).snd.fst[i.val] = both
i_in_bounds : i.val < f.assignments.size
h0 : insertUnit_invariant f.assignments ⋯ f.ratUnits f.assignments ⋯
⊢ p ⊨ c
case intro
n : Nat
f : DefaultFormula n
hf : f.ratUnits = #[] ∧ f.assignments_invariant
c : DefaultClause n
p : PosFin n → Bool
pf : p ⊨ f
insertUnit_fold_success : (List.foldl insertUnit (f.ratUnits, f.assignments, false) c.negate).2.snd = true
i : PosFin n
hboth : (List.foldl insertUnit (f.ratUnits, f.assignments, false) c.negate).snd.fst[i.val] = both
i_in_bounds : i.val < f.assignments.size
h0 : insertUnit_invariant f.assignments ⋯ f.ratUnits f.assignments ⋯
insertUnit_fold_satisfies_invariant :
  let update_res := List.foldl insertUnit (f.ratUnits, f.assignments, false) c.negate;
  let_fun update_res_size := ⋯;
  insertUnit_invariant f.assignments ⋯ update_res.fst update_res.snd.fst update_res_size
⊢ p ⊨ c