let H be LTL-formula; :: thesis: ( H is Until implies H = (the_left_argument_of H) 'U' (the_right_argument_of H) )
assume A1: H is Until ; :: thesis: H = (the_left_argument_of H) 'U' (the_right_argument_of H)
then ex H1 being LTL-formula st H = H1 'U' (the_right_argument_of H) by Def20;
hence H = (the_left_argument_of H) 'U' (the_right_argument_of H) by A1, Def19; :: thesis: verum