reserve n,m,k for Element of NAT;
reserve x, X,X1,Z,Z1 for set;
reserve s,g,r,p,x0,x1,x2 for Real;
reserve s1,s2,q1 for Real_Sequence;
reserve Y for Subset of REAL;
reserve f,f1,f2 for PartFunc of REAL,REAL;

theorem Th50:
  for a,b being Real st a<> 0 holds AffineMap(a,b) is one-to-one
proof
  let a,b be Real such that
A1: a<> 0;
  let x1,x2 be object;
  set f = AffineMap(a,b);
  assume x1 in dom f;
  then reconsider r1 = x1 as Real;
  assume x2 in dom f;
  then reconsider r2 = x2 as Real;
  assume f.x1 = f.x2;
  then a*r1+b = f.x2 by Def4
    .= a*r2 +b by Def4;
  hence thesis by A1,XCMPLX_1:5;
end;
