theorem Th31:
  the_left_side_of(F <=> G) = F & the_right_side_of(F <=> G) = G &
the_left_argument_of(F <=> G) = F => G & the_right_argument_of(F <=> G) = G =>
  F
proof
  the_antecedent_of(F => G) = F & the_consequent_of(F => G) = G by Th30;
  hence thesis by Th4;
end;
