reserve N for Nat;
reserve n,m,n1,n2 for Nat;
reserve q,r,r1,r2 for Real;
reserve x,y for set;
reserve w,w1,w2,g,g1,g2 for Point of TOP-REAL N;
reserve seq,seq1,seq2,seq3,seq9 for Real_Sequence of N;

theorem
  seq1 - (seq2 - seq3) = seq1 - seq2 + seq3
proof
  thus seq1-(seq2-seq3)=seq1+(-1)*(seq2-seq3) by Th11
    .=seq1+((-1)*seq2-((-1)*seq3)) by Th14
    .=seq1+(-seq2-((-1)*seq3)) by Th11
    .=seq1+(-seq2-(-seq3)) by Th11
    .=seq1+(-seq2+seq3) by Th17
    .=seq1-seq2+seq3 by Th10;
end;
