 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 Th26:
  for H1,H2 being non empty SubStr of G st
    the carrier of H1 = the carrier of H2 holds
      the multMagma of H1 = the multMagma of H2
proof
  let H1,H2 be non empty SubStr of G;
A1: op(H2) c= op(G) by Def23;
  op(H1) c= op(G) & dom op(H1) = [:carr(H1), carr(H1):] by Def23,FUNCT_2:def 1;
  then
A2: op(H1) = op(G)||carr(H1) by GRFUNC_1:23;
  assume
A3: carr(H1) = carr(H2);
  then dom op(H2) = [:carr(H1), carr(H1):] by FUNCT_2:def 1;
  hence thesis by A3,A1,A2,GRFUNC_1:23;
end;
