internlm/Lean-Github huggingface dataset:
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ f'.assignments[↑i] = f.assignments[↑i] ∧ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i
Tactic:
constructor
Proof state after:
case inl.intro.h.left
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ f'.assignments[↑i] = f.assignments[↑i]

case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h.left
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ f'.assignments[↑i] = f.assignments[↑i]

case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i
Tactic:
. exact h1
Proof state after:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i
Tactic:
. intro j _
  have idx_in_list : derivedLits_arr[j] ∈ derivedLits := by
    simp only [derivedLits_arr_def, Fin.getElem_fin]
    apply Array.getElem_mem_data
  exact h2 derivedLits_arr[j] idx_in_list
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h.left
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ f'.assignments[↑i] = f.assignments[↑i]
Tactic:
exact h1
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
⊢ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i
Tactic:
intro j _
Proof state after:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
⊢ derivedLits_arr[j].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
⊢ derivedLits_arr[j].fst.val ≠ ↑i
Tactic:
have idx_in_list : derivedLits_arr[j] ∈ derivedLits := by
  simp only [derivedLits_arr_def, Fin.getElem_fin]
  apply Array.getElem_mem_data
Proof state after:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
idx_in_list : derivedLits_arr[j] ∈ derivedLits
⊢ derivedLits_arr[j].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inl.intro.h.right
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
idx_in_list : derivedLits_arr[j] ∈ derivedLits
⊢ derivedLits_arr[j].fst.val ≠ ↑i
Tactic:
exact h2 derivedLits_arr[j] idx_in_list
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
⊢ derivedLits_arr[j] ∈ derivedLits
Tactic:
simp only [derivedLits_arr_def, Fin.getElem_fin]
Proof state after:
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
⊢ { data := derivedLits }[↑j] ∈ derivedLits
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
h1 : f'.assignments[↑i] = f.assignments[↑i]
h2 : ∀ (l : Literal (PosFin n)), l ∈ derivedLits → l.fst.val ≠ ↑i
j : Fin derivedLits_arr.size
a✝ : ↑j ≥ 0
⊢ { data := derivedLits }[↑j] ∈ derivedLits
Tactic:
apply Array.getElem_mem_data
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
⊢ let_fun i_lt_assignments_size := ⋯;
  let_fun i_lt_f_assignments_size := ⋯;
  let assignments_i := f'.assignments[↑i];
  let fassignments_i := f.assignments[↑i];
  (assignments_i = fassignments_i ∧ ∀ (j : Fin derivedLits_arr.size), ↑j ≥ 0 → derivedLits_arr[j].fst.val ≠ ↑i) ∨
    (∃ j b i_gt_zero,
        ↑j ≥ 0 ∧
          derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
            assignments_i = addAssignment b fassignments_i ∧
              ¬hasAssignment b fassignments_i = true ∧
                ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i) ∨
      ∃ j1 j2 i_gt_zero,
        ↑j1 ≥ 0 ∧
          ↑j2 ≥ 0 ∧
            derivedLits_arr[j1] = (⟨↑i, ⋯⟩, true) ∧
              derivedLits_arr[j2] = (⟨↑i, ⋯⟩, false) ∧
                assignments_i = both ∧
                  fassignments_i = unassigned ∧
                    ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j1 → k ≠ j2 → derivedLits_arr[k].fst.val ≠ ↑i
Tactic:
apply Or.inr ∘ Or.inl
Proof state after:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
⊢ ∃ j b i_gt_zero,
    ↑j ≥ 0 ∧
      derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
        f'.assignments[↑i] = addAssignment b f.assignments[↑i] ∧
          ¬hasAssignment b f.assignments[↑i] = true ∧
            ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
⊢ ∃ j b i_gt_zero,
    ↑j ≥ 0 ∧
      derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
        f'.assignments[↑i] = addAssignment b f.assignments[↑i] ∧
          ¬hasAssignment b f.assignments[↑i] = true ∧
            ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i
Tactic:
have j_lt_derivedLits_arr_size : j.1 < derivedLits_arr.size := by
  simp only [derivedLits_arr_def, Array.size_mk]
  exact j.2
Proof state after:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
j_lt_derivedLits_arr_size : ↑j < derivedLits_arr.size
⊢ ∃ j b i_gt_zero,
    ↑j ≥ 0 ∧
      derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
        f'.assignments[↑i] = addAssignment b f.assignments[↑i] ∧
          ¬hasAssignment b f.assignments[↑i] = true ∧
            ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
j_lt_derivedLits_arr_size : ↑j < derivedLits_arr.size
⊢ ∃ j b i_gt_zero,
    ↑j ≥ 0 ∧
      derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
        f'.assignments[↑i] = addAssignment b f.assignments[↑i] ∧
          ¬hasAssignment b f.assignments[↑i] = true ∧
            ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i
Tactic:
have i_gt_zero : i.1 > 0 := by rw [← j_eq_i]; exact (List.get derivedLits j).1.2.1
Proof state after:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
j_lt_derivedLits_arr_size : ↑j < derivedLits_arr.size
i_gt_zero : ↑i > 0
⊢ ∃ j b i_gt_zero,
    ↑j ≥ 0 ∧
      derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
        f'.assignments[↑i] = addAssignment b f.assignments[↑i] ∧
          ¬hasAssignment b f.assignments[↑i] = true ∧
            ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i
Theorem: LRAT.DefaultFormula.restoreAssignments_performRupCheck_base_case
Proof state before:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
j_lt_derivedLits_arr_size : ↑j < derivedLits_arr.size
i_gt_zero : ↑i > 0
⊢ ∃ j b i_gt_zero,
    ↑j ≥ 0 ∧
      derivedLits_arr[j] = (⟨↑i, ⋯⟩, b) ∧
        f'.assignments[↑i] = addAssignment b f.assignments[↑i] ∧
          ¬hasAssignment b f.assignments[↑i] = true ∧
            ∀ (k : Fin derivedLits_arr.size), ↑k ≥ 0 → k ≠ j → derivedLits_arr[k].fst.val ≠ ↑i
Tactic:
refine ⟨⟨j.1, j_lt_derivedLits_arr_size⟩, List.get derivedLits j |>.2, i_gt_zero, ?_⟩
Proof state after:
case inr.inl.intro.intro.intro.intro
rupHints : Array Nat
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
f' : DefaultFormula n
_f'_def : f' = (f.performRupCheck rupHints).fst
f'_assignments_size : f'.assignments.size = n
derivedLits : List (Literal (PosFin n))
derivedLits_arr : Array (Literal (PosFin n))
derivedLits_arr_def : derivedLits_arr = { data := derivedLits }
_derivedLits_arr_nodup : ∀ (i j : Fin derivedLits_arr.size), i ≠ j → derivedLits_arr[i] ≠ derivedLits_arr[j]
i : Fin n
j : Fin derivedLits.length
j_eq_i : (derivedLits.get j).fst.val = ↑i
h1 : f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin derivedLits.length), k ≠ j → (derivedLits.get k).fst.val ≠ ↑i
j_lt_derivedLits_arr_size : ↑j < derivedLits_arr.size
i_gt_zero : ↑i > 0
⊢ ↑⟨↑j, j_lt_derivedLits_arr_size⟩ ≥ 0 ∧
    derivedLits_arr[⟨↑j, j_lt_derivedLits_arr_size⟩] = (⟨↑i, ⋯⟩, (derivedLits.get j).snd) ∧
      f'.assignments[↑i] = addAssignment (derivedLits.get j).snd f.assignments[↑i] ∧
        ¬hasAssignment (derivedLits.get j).snd f.assignments[↑i] = true ∧
          ∀ (k : Fin derivedLits_arr.size),
            ↑k ≥ 0 → k ≠ ⟨↑j, j_lt_derivedLits_arr_size⟩ → derivedLits_arr[k].fst.val ≠ ↑i