reserve U1,U2,U3 for Universal_Algebra,
  m,n for Nat,
  a for set,
  A for non empty set,
  h for Function of U1,U2;

theorem Th11:
  for U1,U2,h st U1,U2 are_similar for o be OperSymbol of MSSign
  U1 holds ((MSAlg h).(the_result_sort_of o)) = h
proof
  let U1,U2,h such that
A1: U1,U2 are_similar;
  set f = MSAlg h;
  let o be OperSymbol of MSSign U1;
A2: the carrier' of MSSign U1 = dom signature U1 & the ResultSort of MSSign
  U1 = dom signature U1-->0 by MSUALG_1:def 8;
A3: 0 in {0} by TARSKI:def 1;
  thus (f.(the_result_sort_of o)) = (f.((the ResultSort of MSSign U1).o)) by
MSUALG_1:def 2
    .= (( 0.--> h ).0 ) by A1,A2,Def3,Th10
    .= h by A3,FUNCOP_1:7;
end;
