reserve F for Field,
  a,b,c,d,e,f,g,h for Element of F;
reserve x,y for Element of [:the carrier of F,the carrier of F,the carrier of
  F:];
reserve F for Field;
reserve PS for non empty ParStr;
reserve x for set,
  a,b,c,d,e,f,g,h,i,j,k,l for Element of [:the carrier of F,
  the carrier of F,the carrier of F:];
reserve a,b,c,d,p,q,r,s for Element of MPS(F);
reserve PS for ParSp,
  a,b,c,d,p,q,r,s for Element of PS;

theorem Th29:
  not a,b '||' a,c implies not a,c '||' a,b & not b,a '||' a,c &
not a,b '||' c,a & not a,c '||' b,a & not b,a '||' c,a & not c,a '||' a,b & not
c,a '||' b,a & not b,a '||' b,c & not a,b '||' b,c & not b,a '||' c,b & not b,c
  '||' b,a & not b,a '||' c,b & not c,b '||' b,a & not b,c '||' a,b & not c,b
  '||' a,b & not c,a '||' c,b & not a,c '||' c,b & not c,a '||' b,c & not a,c
  '||' b,c & not c,b '||' c,a & not b,c '||' c,a & not c,b '||' a,c & not b,c
  '||' a,c
proof
  assume
A1: not a,b '||' a,c;
  assume not thesis;
  then
  a,c '||' a,b or a,b '||' a,c or a,b '||' a,c or a,c '||' a,b or a,b '||'
a,c or a,c '||' a,b or a,c '||' a,b or b,a '||' b,c or b,a '||' b,c or b,a '||'
b,c or b,c '||' b,a or b,a '||' b,c or b,c '||' b,a or b,c '||' b,a or b,c '||'
b,a or c,a '||' c,b or c,a '||' c,b or c,a '||' c,b or c,a '||' c,b or c,b '||'
  c,a or c,b '||' c,a or c,b '||' c,a or c,b '||' c,a by Th23;
  hence contradiction by A1,Th24;
end;
