theorem Th25:
  Suc(f) = All(x,p) & Ant(f) |= Suc(f) implies for y holds Ant(f) |= p.(x,y)
proof
  assume
A1: Suc(f) = All(x,p) & Ant(f) |= Suc(f);
  let y,A,J,v;
  assume J,v |= Ant(f);
  then
A2: J,v |= All(x,p) by A1;
  ex a st v.y = a & J,v.(x|a) |= p
  proof
    take v.y;
    thus thesis by A2,SUBLEMMA:50;
  end;
  hence thesis by Th24;
end;
