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

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