theorem Th14:
  Valid(p '&' 'not' p,J).v = FALSE
proof
A1: now
    assume (Valid(p,J)).v = TRUE;
    then 'not'(Valid(p,J).v) = FALSE by MARGREL1:11;
    hence (Valid(p,J).v) '&' 'not'(Valid(p,J).v) = FALSE by MARGREL1:12;
  end;
A2: Valid(p,J).v = FALSE implies (Valid(p,J).v) '&' 'not' (Valid(p,J).v) =
  FALSE by MARGREL1:12;
  Valid(p '&' 'not' p,J).v = (Valid(p,J).v) '&' (Valid('not' p,J).v) by Th12
    .= (Valid(p,J).v) '&' 'not'(Valid(p,J).v) by Th10;
  hence thesis by A1,A2,XBOOLEAN:def 3;
end;
