reserve x,X for set,
        r,r1,r2,s for Real,
        i,j,k,m,n for Nat;
reserve p,q for Point of TOP-REAL n;

theorem Th28:
 1 <= i & i < j & j <= n implies Mx2Tran Rotation(i,j,n,r) is base_rotation
proof
  assume A1: 1<=i & i<j & j<=n;
  set S=the carrier of TOP-REAL n,G=GFuncs S;
  reconsider M=Mx2Tran Rotation(i,j,n,r) as Element of G by MONOID_0:73;
  take F=<*M*>;
  thus Product F=Mx2Tran Rotation(i,j,n,r) by GROUP_4:9;
  let k;
  assume k in dom F;
  then k in {1} by FINSEQ_1:2,38;
  then A2: k=1 by TARSKI:def 1;
  thus thesis by A1,A2;
end;
