
theorem Th61:
  for S being non empty RelStr, x being Element of S, X being
  Subset of S holds (x "/\").:X = {x"/\"y where y is Element of S: y in X}
proof
  let S be non empty RelStr, x be Element of S, X be Subset of S;
  set Y = {x"/\"y where y is Element of S: y in X};
  hereby
    let y be object;
    assume y in (x "/\").:X;
    then consider z being object such that
A1: z in the carrier of S and
A2: z in X and
A3: y = (x "/\").z by FUNCT_2:64;
    reconsider z as Element of S by A1;
    y = x "/\" z by A3,Def18;
    hence y in Y by A2;
  end;
  let y be object;
  assume y in Y;
  then consider z being Element of S such that
A4: y = x "/\" z and
A5: z in X;
  y = (x "/\").z by A4,Def18;
  hence thesis by A5,FUNCT_2:35;
end;
