
theorem Th2: :: MSAFREE:5
  for S being non void non empty ManySortedSign, X being
ManySortedSet of the carrier of S
for o,b being object st [o,b] in REL(X) holds o
  in [:the carrier' of S,{the carrier of S}:] & b in ([:the carrier' of S,{the
  carrier of S}:] \/ Union coprod X)*
proof
  let S be non void non empty ManySortedSign, X be ManySortedSet of the
  carrier of S;
  let o,b be object;
  assume
A1: [o,b] in REL(X);
  then reconsider
  o9=o as Element of [:the carrier' of S,{the carrier of S}:] \/
  Union(coprod X) by ZFMISC_1:87;
  reconsider b9=b as Element of ([:the carrier' of S,{the carrier of S}:] \/
  Union(coprod X))* by A1,ZFMISC_1:87;
A2: [o9,b9] in REL(X) by A1;
  hence o in [:the carrier' of S,{the carrier of S}:] by MSAFREE:def 7;
  thus thesis by A2;
end;
