reserve S for non empty non void ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S,
  A for non-empty MSAlgebra over S,
  X for non empty Subset of S-Terms V,
  t for Element of X;
reserve S for non empty non void ManySortedSign,
  A for non-empty finite-yielding MSAlgebra over S,
  V for Variables of A,
  X for SetWithCompoundTerm of S,V;
reserve G1, G2 for Circuit-like non void non empty ManySortedSign,
  f, g for Function,
  C1 for non-empty Circuit of G1,
  C2 for non-empty Circuit of G2;

theorem Th41:
  f, g form_embedding_of C1, C2 implies
  dom f = the carrier of G1 & rng f c= the carrier of G2 &
  dom g = the carrier' of G1 & rng g c= the carrier' of G2
proof
  assume that f is one-to-one and g is one-to-one and
A1: dom f = the carrier of G1 and
A2: dom g = the carrier' of G1 and
A3: rng f c= the carrier of G2 and
A4: rng g c= the carrier' of G2;
  thus thesis by A1,A2,A3,A4;
end;
