theorem
  M,v |= (p => r) '&' (q => r) => (p 'or' q => r) & M |= (p => r) '&' (q
  => r) => (p 'or' q => r)
proof
  now
    let v;
    now
      assume M,v |= (p => r) '&' (q => r);
      then M,v |= p => r & M,v |= q => r by ZF_MODEL:15;
      then M,v |= p or M,v |= q implies M,v |= r by ZF_MODEL:18;
      then M,v |= p 'or' q implies M,v |= r by ZF_MODEL:17;
      hence M,v |= p 'or' q => r by ZF_MODEL:18;
    end;
    hence M,v |= (p => r) '&' (q => r) => (p 'or' q => r) by ZF_MODEL:18;
  end;
  hence thesis;
end;
