reserve m,n for Nat;
reserve i,j for Integer;
reserve S for non empty addMagma;
reserve r,r1,r2,s,s1,s2,t,t1,t2 for Element of S;
reserve G for addGroup-like non empty addMagma;
reserve e,h for Element of G;
reserve G for addGroup;
reserve f,g,h for Element of G;
reserve u for UnOp of G;

theorem Th31:
  (-1) * h = -h
proof
  |.-1.| = - (-1) by ABSVALUE:def 1;
  hence (-1) * h = -( 1 * h) by Def8
    .= -h by Th25;
end;
