internlm/Lean-Github huggingface dataset:
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
⊢ ∀ (i : PosFin n) (b : Bool),
    hasAssignment b
          { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
                assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
        true →
      unit (i, b) ∈
        { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
intro i b hb
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
have hf := f_readyForRupAdd.2.2 i b
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
have i_in_bounds : i.1 < f.assignments.size := by rw [f_readyForRupAdd.2.1]; exact i.2.2
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
have l_in_bounds : l.1 < f.assignments.size := by rw [f_readyForRupAdd.2.1]; exact l.2.2
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
simp only at hb
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
by_cases (i, b) = (l, true)
Proof state after:
case pos
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : (i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList

case neg
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : ¬(i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
case pos
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : (i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList

case neg
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : ¬(i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
. next ib_eq_c =>
  simp only [toList, Array.toList_eq, Array.push_data, List.append_assoc, List.mem_append, List.mem_filterMap,
    List.mem_singleton, id_eq, exists_eq_right, Option.some.injEq, List.mem_map, Prod.exists, Bool.exists_bool]
  apply Or.inl ∘ Or.inr
  rw [isUnit_iff, DefaultClause.toList, ← ib_eq_c] at hc
  apply DefaultClause.ext
  simp only [unit, hc]
Proof state after:
case neg
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : ¬(i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
case neg
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : ¬(i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
. next ib_ne_c =>
  have hb' : hasAssignment b (f.assignments[i.1]'i_in_bounds) := by
    by_cases l.1 = i.1
    . next l_eq_i =>
      have b_eq_false : b = false := by
        by_cases b = true
        . next b_eq_true =>
          simp only [b_eq_true, Subtype.ext l_eq_i, not_true] at ib_ne_c
        . next b_eq_false =>
          simp only [Bool.not_eq_true] at b_eq_false
          exact b_eq_false
      simp only [hasAssignment, b_eq_false, l_eq_i, Array.get_modify_at_idx i_in_bounds, ite_false, hasNeg_of_addPos] at hb
      simp only [hasAssignment, b_eq_false, ite_false, hb]
    . next l_ne_i =>
      simp only [Array.get_modify_unchanged l_in_bounds i_in_bounds _ l_ne_i] at hb
      exact hb
  specialize hf hb'
  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] at hf
  simp only [toList, Array.toList_eq, Array.push_data, List.append_assoc, List.mem_append, List.mem_filterMap,
    List.mem_singleton, id_eq, exists_eq_right, Option.some.injEq, List.mem_map, Prod.exists, Bool.exists_bool]
  rcases hf with hf | hf
  . exact Or.inl $ Or.inl hf
  . exact Or.inr hf
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
⊢ (f.assignments.modify l.val addPosAssignment).size = n
Tactic:
rw [Array.modify_preserves_size, f_readyForRupAdd.2.1]
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
⊢ i.val < f.assignments.size
Tactic:
rw [f_readyForRupAdd.2.1]
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
⊢ i.val < n
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
⊢ i.val < n
Tactic:
exact i.2.2
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
⊢ l.val < f.assignments.size
Tactic:
rw [f_readyForRupAdd.2.1]
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
⊢ l.val < n
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb :
  hasAssignment b
      { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
            assignments := f.assignments.modify l.val addPosAssignment }.assignments[i.val] =
    true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
⊢ l.val < n
Tactic:
exact l.2.2
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
case pos
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
h✝ : (i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
next ib_eq_c =>
simp only [toList, Array.toList_eq, Array.push_data, List.append_assoc, List.mem_append, List.mem_filterMap,
  List.mem_singleton, id_eq, exists_eq_right, Option.some.injEq, List.mem_map, Prod.exists, Bool.exists_bool]
apply Or.inl ∘ Or.inr
rw [isUnit_iff, DefaultClause.toList, ← ib_eq_c] at hc
apply DefaultClause.ext
simp only [unit, hc]
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
ib_eq_c : (i, b) = (l, true)
⊢ unit (i, b) ∈
    { clauses := f.clauses.push (some c), rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.val addPosAssignment }.toList
Tactic:
simp only [toList, Array.toList_eq, Array.push_data, List.append_assoc, List.mem_append, List.mem_filterMap,
  List.mem_singleton, id_eq, exists_eq_right, Option.some.injEq, List.mem_map, Prod.exists, Bool.exists_bool]
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
ib_eq_c : (i, b) = (l, true)
⊢ (some (unit (i, b)) ∈ f.clauses.data ∨ unit (i, b) = c) ∨
    (∃ a,
        (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = unit (i, b) ∨
          (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = unit (i, b)) ∨
      ∃ a,
        (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = unit (i, b) ∨
          (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = unit (i, b)
Theorem: LRAT.DefaultFormula.insert_readyForRupAdd
Proof state before:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
ib_eq_c : (i, b) = (l, true)
⊢ (some (unit (i, b)) ∈ f.clauses.data ∨ unit (i, b) = c) ∨
    (∃ a,
        (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = unit (i, b) ∨
          (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = unit (i, b)) ∨
      ∃ a,
        (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = unit (i, b) ∨
          (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = unit (i, b)
Tactic:
apply Or.inl ∘ Or.inr
Proof state after:
n : Nat
f : DefaultFormula n
c : DefaultClause n
f_readyForRupAdd : f.readyForRupAdd
x✝ : Option (Literal (PosFin n))
l : PosFin n
hc : c.isUnit = some (l, true)
hsize : (f.assignments.modify l.val addPosAssignment).size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.assignments.modify l.val addPosAssignment)[i.val] = true
hf : hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
i_in_bounds : i.val < f.assignments.size
l_in_bounds : l.val < f.assignments.size
ib_eq_c : (i, b) = (l, true)
⊢ unit (i, b) = c