theorem Th12:
  len G.walkOf(v) = 1 & G.walkOf(v).1 = v & G.walkOf(v).first() =
  v & G.walkOf(v).last() = v & G.walkOf(v) is_Walk_from v,v
proof
  thus
A1: len G.walkOf(v) = 1 & G.walkOf(v).1 = v by FINSEQ_1:40;
  thus
 G.walkOf(v).first() = v;
  thus G.walkOf(v).last() = v by A1;
  hence thesis;
end;
