theorem Th56:
  injection(H,i).g = [* i, g *]
proof
  set C = the carrier of H.i;
  A1: <*[i,g]*> in [* i,g *] by Th48;
  dom commute <*<:C-->i,id C :>*> = C by Th53;
  hence injection(H,i).g = (proj Class EqCl ReductionRel H).
      ((commute <*<:C-->i,id C :>*>).g) by FUNCT_1:13
    .= (proj Class EqCl ReductionRel H).<*[i,g]*> by Th54
    .= [* i,g *] by A1, EQREL_1:65;
end;
