 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem Th35:
  G is cancelable implies H is cancelable
proof
  assume
A1: G is cancelable;
A2: carr(H) c= carr(G) by Th23;
  now
    let a,b,c be Element of H;
    reconsider a9 = a, b9 = b, c9 = c as Element of G by A2;
A3: b*a = b9*a9 & c*a = c9*a9 by Th25;
    a*b = a9*b9 & a*c = a9*c9 by Th25;
    hence a*b = a*c or b*a = c*a implies b = c by A1,A3,Th13;
  end;
  hence thesis by Th13;
end;
