theorem
  s ==>* t, S & u ==>* v, S implies s^u ==>* t^v, S & u^s ==>* v^t, S
proof
  assume
A1: s ==>* t, S & u ==>* v, S;
  then s^u ==>* t^u, S & t^u ==>* t^v, S by Th36;
  hence s^u ==>* t^v, S by Th35;
  u^s ==>* u^t, S & u^t ==>* v^t, S by A1,Th36;
  hence thesis by Th35;
end;
