show (q * n_k + p * m_j)——(q * m_j + p * n_k)
   ≃ ((qn + pm) + (qk + pj))——((qm + pn) + (qj + pk))
ℕ : Type
inst✝ : Natural ℕ
q p n m k j : ℕ
n_k : ℕ := n + k
m_j : ℕ := m + j
qn : ℕ := q * n
qm : ℕ := q * m
qk : ℕ := q * k
qj : ℕ := q * j
pn : ℕ := p * n
pm : ℕ := p * m
pk : ℕ := p * k
pj : ℕ := p * j
⊢ q——p * n_k——m_j ≃ (qn + pm)——(qm + pn) + (qk + pj)——(qj + pk)
ℕ : Type
inst✝ : Natural ℕ
q p n m k j : ℕ
n_k : ℕ := n + k
m_j : ℕ := m + j
qn : ℕ := q * n
qm : ℕ := q * m
qk : ℕ := q * k
qj : ℕ := q * j
pn : ℕ := p * n
pm : ℕ := p * m
pk : ℕ := p * k
pj : ℕ := p * j
⊢ (q * n_k + p * m_j)——(q * m_j + p * n_k) ≃ (qn + pm + (qk + pj))——(qm + pn + (qj + pk))