
theorem MMcon3:
for f,g be Function of REAL,REAL,
a being Real st
g is continuous & for x be Real holds f.x= max(a, g.x)
holds f is continuous
proof
 let f,g be Function of REAL,REAL;
 let a be Real;
 assume A3: g is continuous;
 assume A0:for x be Real holds f.x= max(a, g.x);
 consider h being Function of REAL,REAL such that
 A2: h = AffineMap (0,a);
 for x be Real holds f.x= max(h.x, g.x)
 proof
  let x be Real;
  f.x=max(0*x+a, g.x) by A0
  .=max(AffineMap (0,a).x, g.x) by FCONT_1:def 4;
  hence thesis by A2;
 end;
 hence thesis by MMcon2,A3,A2;
end;
