reserve k, n for Nat;

theorem Th1:
  for S being ManySortedSign holds InducedEdges S c= [: the
  carrier' of S, the carrier of S :]
proof
  let S be ManySortedSign;
  let x be object;
  assume x in InducedEdges S;
  then ex op, v being set st x = [op, v] & op in the carrier' of S & v in the
  carrier of S & ex n being Nat, args being Element of (the carrier of S)* st (
  the Arity of S).op = args & n in dom args & args.n = v by Def1;
  hence thesis by ZFMISC_1:def 2;
end;
