theorem Th46: :: PDIFF_7:46

for m being non zero Nat
for h being FinSequence of REAL m
for y, x being Element of REAL m
for j being Nat st len h = m + 1 & 1 <= j & j <= m & ( for i being Nat st i in dom h holds
h /. i = (y | ((m + 1) -' i)) ^ (0* (i -' 1)) ) holds
x + (h /. j) = (reproj (((m + 1) -' j),(x + (h /. (j + 1))))) . ((proj (((m + 1) -' j),m)) . (x + y))