
theorem Th30:
  for S being 1-sorted, M being set holds Carrier (M --> S) = M
  --> the carrier of S
proof
  let S be 1-sorted, M be set;
  now
    let i be object;
    assume
A1: i in M;
    then
    (M --> S).i = S & ex R being 1-sorted st R = (M --> S).i & (Carrier (M
    --> S )).i = the carrier of R by FUNCOP_1:7,PRALG_1:def 15;
    hence (Carrier (M --> S)).i = (M --> the carrier of S).i by A1,FUNCOP_1:7;
  end;
  hence thesis by PBOOLE:3;
end;
