reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem Th23:
  a<>b & ( a,b '||' x,y & a,b '||' z,t or a,b '||' x,y & z,t '||'
a,b or x,y '||' a,b & z,t '||' a,b or x,y '||' a,b & a,b '||' z,t ) implies x,y
  '||' z,t
proof
  assume that
A1: a<>b and
A2: a,b '||' x,y & a,b '||' z,t or a,b '||' x,y & z,t '||' a,b or x,y
  '||' a,b & z,t '||' a,b or x,y '||' a,b & a,b '||' z,t;
  a,b '||' x,y & a,b '||' z,t by A2,Th22;
  hence thesis by A1,Lm2;
end;
