have e1 : a = b, from H1,
have e2 : a = c, from e1 ⬝ H2,
have e3 : c = a, from e2⁻¹,
have e4 : 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