reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;
reserve p,q for natural Number;
reserve i0,i,i1,i2,i4 for Integer;
reserve x for set;
reserve p for Prime;
reserve i for Nat;
reserve x for Real;
reserve k for Nat;
reserve k,n,n1,n2,m1,m2 for Nat;

theorem
  (2|^n1)*(2*m1+1) = (2|^n2)*(2*m2+1) implies n1 = n2 & m1 = m2
proof
A1: 2|^n1 <> 0 by Th87;
  assume
A2: (2|^n1)*(2*m1+1) = (2|^n2)*(2*m2+1);
  then
A3: n2 <= n1 by Lm5;
  n1 <= n2 by A2,Lm5;
  hence n1 = n2 by A3,XXREAL_0:1;
  then 2*m1+1 = 2*m2+1 by A2,A1,XCMPLX_1:5;
  hence thesis;
end;
