reserve r, r1, r2, x, y, z,
        x1, x2, x3, y1, y2, y3 for Real;
reserve R, R1, R2, R3 for Element of 3-tuples_on REAL;
reserve p, q, p1, p2, p3, q1, q2 for Element of REAL 3;
reserve f1, f2, f3, g1, g2, g3, h1, h2, h3 for PartFunc of REAL,REAL;
reserve t, t0, t1, t2 for Real;

theorem
  (f1 is_differentiable_in t0 & f2 is_differentiable_in t0 &
  f3 is_differentiable_in t0) & (g1 is_differentiable_in t0 &
  g2 is_differentiable_in t0 & g3 is_differentiable_in t0) &
  (h1 is_differentiable_in t0 & h2 is_differentiable_in t0 &
   h3 is_differentiable_in t0) implies
  VFuncdiff( h2(#)f2(#)g3-h3(#)f3(#)g2,
             h3(#)f3(#)g1-h1(#)f1(#)g3,
             h1(#)f1(#)g2-h2(#)f2(#)g1,t0 )
  = |[ (h2.t0)*(f2.t0)*diff(g3,t0)-(h3.t0)*(f3.t0)*diff(g2,t0),
       (h3.t0)*(f3.t0)*diff(g1,t0)-(h1.t0)*(f1.t0)*diff(g3,t0),
       (h1.t0)*(f1.t0)*diff(g2,t0)-(h2.t0)*(f2.t0)*diff(g1,t0) ]|+
    |[ (h2.t0)*diff(f2,t0)*(g3.t0)-(h3.t0)*diff(f3,t0)*(g2.t0),
       (h3.t0)*diff(f3,t0)*(g1.t0)-(h1.t0)*diff(f1,t0)*(g3.t0),
       (h1.t0)*diff(f1,t0)*(g2.t0)-(h2.t0)*diff(f2,t0)*(g1.t0) ]|+
    |[ diff(h2,t0)*(f2.t0)*(g3.t0)-diff(h3,t0)*(f3.t0)*(g2.t0),
       diff(h3,t0)*(f3.t0)*(g1.t0)-diff(h1,t0)*(f1.t0)*(g3.t0),
       diff(h1,t0)*(f1.t0)*(g2.t0)-diff(h2,t0)*(f2.t0)*(g1.t0) ]|
proof
  assume that
A1: f1 is_differentiable_in t0 & f2 is_differentiable_in t0 &
    f3 is_differentiable_in t0 and
A2: g1 is_differentiable_in t0 & g2 is_differentiable_in t0 &
    g3 is_differentiable_in t0 and
A3: h1 is_differentiable_in t0 &
    h2 is_differentiable_in t0 & h3 is_differentiable_in t0;
A4: h3(#)f3 is_differentiable_in t0 & h1(#)f1 is_differentiable_in t0 &
    h2(#)f2 is_differentiable_in t0 by A1,A3,FDIFF_1:16;
then A5: h3(#)f3(#)g1 is_differentiable_in t0 &
    h3(#)f3(#)g2 is_differentiable_in t0 &
    h1(#)f1(#)g2 is_differentiable_in t0 &
    h1(#)f1(#)g3 is_differentiable_in t0 &
    h2(#)f2(#)g3 is_differentiable_in t0 &
    h2(#)f2(#)g1 is_differentiable_in t0 by A2,FDIFF_1:16;
 VFuncdiff( h2(#)f2(#)g3-h3(#)f3(#)g2, h3(#)f3(#)g1-h1(#)f1(#)g3,
             h1(#)f1(#)g2-h2(#)f2(#)g1,t0 )
 = VFuncdiff( h2(#)f2(#)g3,h3(#)f3(#)g1,h1(#)f1(#)g2,t0 )-
   VFuncdiff( h3(#)f3(#)g2,h1(#)f1(#)g3,h2(#)f2(#)g1,t0 ) by A5,Th89
.= |[ (g3.t0)*diff(h2(#)f2,t0),(g1.t0)*diff(h3(#)f3,t0),
      (g2.t0)*diff(h1(#)f1,t0) ]|+
   |[ (h2(#)f2).t0*diff(g3,t0),(h3(#)f3).t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   VFuncdiff( h3(#)f3(#)g2,h1(#)f1(#)g3,h2(#)f2(#)g1,t0 ) by A2,A4,Th91
.= |[ (g3.t0)*diff(h2(#)f2,t0),(g1.t0)*diff(h3(#)f3,t0),
      (g2.t0)*diff(h1(#)f1,t0) ]|+
   |[ (h2(#)f2).t0*diff(g3,t0),(h3(#)f3).t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by A2,A4,Th91
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*diff(h3(#)f3,t0),(g2.t0)*diff(h1(#)f1,t0) ]|+
   |[ (h2(#)f2).t0*diff(g3,t0),(h3(#)f3).t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by A1,A3,FDIFF_1:16
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*diff(h1(#)f1,t0) ]|+
   |[ (h2(#)f2).t0*diff(g3,t0),(h3(#)f3).t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by A1,A3,FDIFF_1:16
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ (h2(#)f2).t0*diff(g3,t0),(h3(#)f3).t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by A1,A3,FDIFF_1:16
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),(h3(#)f3).t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by VALUED_1:5
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      (h1(#)f1).t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by VALUED_1:5
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ (h3(#)f3).t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by VALUED_1:5
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ h3.t0*f3.t0*diff(g2,t0),(h1(#)f1).t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by VALUED_1:5
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      (h2(#)f2).t0*diff(g1,t0) ]|) by VALUED_1:5
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*diff(h3(#)f3,t0),(g3.t0)*diff(h1(#)f1,t0),
      (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]|) by VALUED_1:5
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*diff(h1(#)f1,t0),(g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]|) by A1,A3,FDIFF_1:16
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
     (g1.t0)*diff(h2(#)f2,t0) ]|+
   |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]|) by A1,A3,FDIFF_1:16
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   (|[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
     (g1.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)) ]|+
   |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]|) by A1,A3,FDIFF_1:16
.= |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
   |[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
     (g1.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)) ]|-
   |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]| by RVSUM_1:39
.= (|[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|-
   |[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
     (g1.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)) ]|)+
   |[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|+
   -|[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]| by RVSUM_1:15
.= (|[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|-
   |[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
     (g1.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)) ]|)+
   (|[ h2.t0*f2.t0*diff(g3,t0),h3.t0*f3.t0*diff(g1,t0),
      h1.t0*f1.t0*diff(g2,t0) ]|-
    |[ h3.t0*f3.t0*diff(g2,t0),h1.t0*f1.t0*diff(g3,t0),
      h2.t0*f2.t0*diff(g1,t0) ]|) by RVSUM_1:15
.= (|[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)) ]|-
   |[ (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
     (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
     (g1.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)) ]|)+
   |[ h2.t0*f2.t0*diff(g3,t0)-h3.t0*f3.t0*diff(g2,t0),
       h3.t0*f3.t0*diff(g1,t0)-h1.t0*f1.t0*diff(g3,t0),
       h1.t0*f1.t0*diff(g2,t0)-h2.t0*f2.t0*diff(g1,t0) ]| by Lm11
.= |[  h2.t0*f2.t0*diff(g3,t0)-h3.t0*f3.t0*diff(g2,t0),
       h3.t0*f3.t0*diff(g1,t0)-h1.t0*f1.t0*diff(g3,t0),
       h1.t0*f1.t0*diff(g2,t0)-h2.t0*f2.t0*diff(g1,t0) ]|+
   |[ (g3.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0))-
       (g2.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0)),
      (g1.t0)*((f3.t0)*diff(h3,t0)+(h3.t0)*diff(f3,t0))-
      (g3.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0)),
      (g2.t0)*((f1.t0)*diff(h1,t0)+(h1.t0)*diff(f1,t0))-
      (g1.t0)*((f2.t0)*diff(h2,t0)+(h2.t0)*diff(f2,t0)) ]| by Lm11
.= |[  h2.t0*f2.t0*diff(g3,t0)-h3.t0*f3.t0*diff(g2,t0),
       h3.t0*f3.t0*diff(g1,t0)-h1.t0*f1.t0*diff(g3,t0),
       h1.t0*f1.t0*diff(g2,t0)-h2.t0*f2.t0*diff(g1,t0) ]|+
   |[ ((g3.t0)*(h2.t0)*diff(f2,t0)-(g2.t0)*(h3.t0)*diff(f3,t0))
      +((g3.t0)*(f2.t0)*diff(h2,t0)-(g2.t0)*(f3.t0)*diff(h3,t0)),
      ((g1.t0)*(h3.t0)*diff(f3,t0)-(g3.t0)*(h1.t0)*diff(f1,t0))
      +((g1.t0)*(f3.t0)*diff(h3,t0)-(g3.t0)*(f1.t0)*diff(h1,t0)),
      ((g2.t0)*(h1.t0)*diff(f1,t0)-(g1.t0)*(h2.t0)*diff(f2,t0))
      +((g2.t0)*(f1.t0)*diff(h1,t0)-(g1.t0)*(f2.t0)*diff(h2,t0)) ]|
.= |[  h2.t0*f2.t0*diff(g3,t0)-h3.t0*f3.t0*diff(g2,t0),
       h3.t0*f3.t0*diff(g1,t0)-h1.t0*f1.t0*diff(g3,t0),
       h1.t0*f1.t0*diff(g2,t0)-h2.t0*f2.t0*diff(g1,t0) ]|+
   (|[ (g3.t0)*(h2.t0)*diff(f2,t0)-(g2.t0)*(h3.t0)*diff(f3,t0),
      (g1.t0)*(h3.t0)*diff(f3,t0)-(g3.t0)*(h1.t0)*diff(f1,t0),
      (g2.t0)*(h1.t0)*diff(f1,t0)-(g1.t0)*(h2.t0)*diff(f2,t0) ]|+
  |[ (g3.t0)*(f2.t0)*diff(h2,t0)-(g2.t0)*(f3.t0)*diff(h3,t0),
     (g1.t0)*(f3.t0)*diff(h3,t0)-(g3.t0)*(f1.t0)*diff(h1,t0),
     (g2.t0)*(f1.t0)*diff(h1,t0)-(g1.t0)*(f2.t0)*diff(h2,t0) ]|) by Lm8
.= |[  h2.t0*f2.t0*diff(g3,t0)-h3.t0*f3.t0*diff(g2,t0),
       h3.t0*f3.t0*diff(g1,t0)-h1.t0*f1.t0*diff(g3,t0),
       h1.t0*f1.t0*diff(g2,t0)-h2.t0*f2.t0*diff(g1,t0) ]|+
   |[ (g3.t0)*(h2.t0)*diff(f2,t0)-(g2.t0)*(h3.t0)*diff(f3,t0),
      (g1.t0)*(h3.t0)*diff(f3,t0)-(g3.t0)*(h1.t0)*diff(f1,t0),
      (g2.t0)*(h1.t0)*diff(f1,t0)-(g1.t0)*(h2.t0)*diff(f2,t0) ]|+
  |[ (g3.t0)*(f2.t0)*diff(h2,t0)-(g2.t0)*(f3.t0)*diff(h3,t0),
     (g1.t0)*(f3.t0)*diff(h3,t0)-(g3.t0)*(f1.t0)*diff(h1,t0),
     (g2.t0)*(f1.t0)*diff(h1,t0)-(g1.t0)*(f2.t0)*diff(h2,t0) ]|
     by RVSUM_1:15;
  hence thesis;
end;
