Prove that, for all boolean expressions b and all commands c, [while b do cllcomm = [while b do (c; if b then c else skip)]comm. Using the coincidence theorem for commands (Proposition 2.6 in Section...

Prove that, for all boolean expressions b and all commands c, [while b do cllcomm = [while b do (c; if b then c else skip)]comm. Using the coincidence theorem for commands (Proposition 2.6 in Section 2.5), prove that, for all commands co and cl, if FVcomm(co) n FA(cl) = FA(co) n FVcomm(cl) then [co; Clllcomm = [C1; CoIcomm'