have e1 [visible] : a = b, from H1,
have e2 : a = c, from e1 ⬝ H2,
have e3 : c = a, from e2 ⁻¹,
have e4 [visible] : b = a, from e1 ⁻¹,
have e5 : b = c, from e4 ⬝ e2,
have e6 : a = a, from H1 ⬝ H2 ⬝ H2 ⁻¹ ⬝ H1 ⁻¹ ⬝ H1 ⬝ H2 ⬝ H2 ⁻¹ ⬝ H1 ⁻¹,
e3 ⬝ e2 :
  c = c