-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/LRAT/Internal/Formula/RatAddResult.lean
theorem ratAdd_result {n : Nat} (f : DefaultFormula n) (c : DefaultClause n) (p : Literal (PosFin n))
  (rupHints : Array Nat) (ratHints : Array (Nat × Array Nat)) (f' : DefaultFormula n)
  (f_readyForRatAdd : ReadyForRatAdd f) (_pc : p ∈ Clause.toList c)
  (ratAddSuccess : performRatAdd f c p rupHints ratHints = (f', true)) : f' = insert f c

Proof state:
n : Nat
f : DefaultFormula n
c : DefaultClause n
p : Literal (PosFin n)
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
f' : DefaultFormula n
f_readyForRatAdd : f.ReadyForRatAdd
_pc : p ∈ Clause.toList c
h✝³ : f.ratHintsExhaustive p ratHints = true
h✝² : ¬(f.insertRupUnits c.negate).snd = true
h✝¹ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.snd = true
h✝ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.fst = true
ratAddSuccess :
  ({
              clauses :=
                (Array.foldl
                      (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                      (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.clauses,
              rupUnits :=
                (Array.foldl
                      (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                      (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.rupUnits,
              ratUnits :=
                (Array.foldl
                      (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                      (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.ratUnits,
              assignments :=
                restoreAssignments
                  (Array.foldl
                        (fun x ratHint =>
                          if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.assignments
                  ((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.fst }.clearRupUnits.insert
        c,
      true) =
    (f', true)
performRatCheck_fold_success :
  (Array.foldl (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).snd =
    true
fc : DefaultFormula n := (f.insertRupUnits c.negate).fst
fc_assignments_size : (f.insertRupUnits c.negate).fst.assignments.size = n
⊢ f' = f.insert c

Tactic:
simp only [clauses_performRupCheck, rupUnits_performRupCheck, ratUnits_performRupCheck,
  restoreAssignments_performRupCheck fc fc_assignments_size, Prod.mk.injEq, and_true] at ratAddSuccess

Result:
n : Nat
f : DefaultFormula n
c : DefaultClause n
p : Literal (PosFin n)
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
f' : DefaultFormula n
f_readyForRatAdd : f.ReadyForRatAdd
_pc : p ∈ Clause.toList c
h✝³ : f.ratHintsExhaustive p ratHints = true
h✝² : ¬(f.insertRupUnits c.negate).snd = true
h✝¹ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.snd = true
h✝ : ¬((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.2.fst = true
performRatCheck_fold_success :
  (Array.foldl (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
        (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).snd =
    true
fc : DefaultFormula n := (f.insertRupUnits c.negate).fst
fc_assignments_size : (f.insertRupUnits c.negate).fst.assignments.size = n
ratAddSuccess :
  {
            clauses :=
              (Array.foldl
                    (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                    (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.clauses,
            rupUnits :=
              (Array.foldl
                    (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                    (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.rupUnits,
            ratUnits :=
              (Array.foldl
                    (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                    (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.ratUnits,
            assignments :=
              restoreAssignments
                (Array.foldl
                      (fun x ratHint => if x.snd = true then x.fst.performRatCheck p.negate ratHint else (x.fst, false))
                      (((f.insertRupUnits c.negate).fst.performRupCheck rupHints).fst, true) ratHints).1.assignments
                ((f.insertRupUnits c.negate).fst.performRupCheck rupHints).2.fst }.clearRupUnits.insert
      c =
    f'
⊢ f' = f.insert c