
theorem Th14:
  for L being 1-sorted for A,B being AlgebraStr over L st
  the AlgebraStr of A = the AlgebraStr of B holds A is Subalgebra of B
proof
  let L be 1-sorted;
  let A,B be AlgebraStr over L such that
A1: the AlgebraStr of A = the AlgebraStr of B;
  thus the carrier of A c= the carrier of B by A1;
  thus 1.A = 1.B by A1;
  thus 0.A = 0.B by A1;
  thus the addF of A = (the addF of B)||the carrier of A by A1;
  thus the multF of A = (the multF of B)||the carrier of A by A1;
  thus thesis by A1;
end;
