 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 Th25:
  for a,b being Element of H, a9,b9 being Element of G st
    a = a9 & b = b9 holds a*b = a9*b9
proof
  let a,b be Element of H, a9,b9 be Element of G such that
A1: a = a9 & b = b9;
A2: dom op(H) = [:carr(H), carr(H):] & op(H) c= op(G) by Def23,FUNCT_2:def 1;
  thus a*b = op(H).[a,b] .= a9*b9 by A1,A2,GRFUNC_1:2;
end;
