reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem Th76:
  x in A & not y in A implies <* x,y *> - A = <* y *>
proof
  assume that
A1: x in A and
A2: not y in A;
A3: <* y *> - A = <* y *> by A2,Lm6;
A4: <* x,y *> = <* x *> ^ <* y *> by FINSEQ_1:def 9;
  <* x *> - A = {} by A1,Lm7;
  hence <* x,y *> - A = {} ^ <* y *> by A3,A4,Lm11
    .= <* y *> by FINSEQ_1:34;
end;
