theorem Th5: :: PARSP_2:5

for F being Field
for a, b, c, d being Element of (MPS F)
for e, f, g, h being Element of [: the carrier of F, the carrier of F, the carrier of F:] st not a,b '||' a,c & a,b '||' c,d & a,c '||' b,d & [[a,b],[c,d]] = [[e,f],[g,h]] holds
( h `1_3 = ((f `1_3) + (g `1_3)) - (e `1_3) & h `2_3 = ((f `2_3) + (g `2_3)) - (e `2_3) & h `3_3 = ((f `3_3) + (g `3_3)) - (e `3_3) )