
theorem Thm25:
  for A being Point of TOP-REAL 2,a,b be Real, r be positive Real st
  A in circle(a,b,r) holds A <> |[a,b]|
  proof
    let A be Point of TOP-REAL 2,a,b be Real,r be positive Real such that
A1: A in circle(a,b,r);
    circle(a,b,r)={p where p is Point of TOP-REAL 2: |.p-|[a,b]|.|=r}
    by JGRAPH_6:def 5;
    then consider p0 be Point of TOP-REAL 2 such that
A2: A=p0 and
A3: |.p0-|[a,b]|.|=r by A1;
    thus thesis by A2,A3,EUCLID_6:42;
  end;
