
theorem asymTT10:
for a,b,p,q,s be Real holds
( AffineMap (a,b)|].-infty,s.[ ) +* ( AffineMap (p,q)|[.s,+infty.[ )
is Function of REAL,REAL
proof
 let a,b,p,q,s be Real;
 set g = ( ((AffineMap (a,b))|(].-infty,s.[)) +*
                      ((AffineMap (p,q))|([.s,+infty.[)) );
 set g1= ( (AffineMap (a,b))|(].-infty,s.[) );
 set g2= ( (AffineMap (p,q))|([.s,+infty.[) );
 D3: -infty < s & s < +infty by XXREAL_0:9,XXREAL_0:12,XREAL_0:def 1;
  Dg: dom g = (dom g1) \/ (dom g2) by FUNCT_4:def 1
 .= (].-infty,s.[) \/ (dom g2) by FUNCT_2:def 1
 .=(].-infty,s.[) \/ ([.s,+infty.[) by FUNCT_2:def 1
 .=REAL by XXREAL_1:224,XXREAL_1:173,D3;
 for x being object st x in REAL holds g . x in REAL by XREAL_0:def 1;
 hence thesis by FUNCT_2:3,Dg;
end;
