let n be Nat; for RAS being ReperAlgebra of n
for a being Point of RAS
for p being Tuple of (n + 1),RAS
for W being ATLAS of RAS
for x being Tuple of (n + 1),W st (a,x) . W = p holds
Phi x = W . (a,(*' (a,p)))
let RAS be ReperAlgebra of n; for a being Point of RAS
for p being Tuple of (n + 1),RAS
for W being ATLAS of RAS
for x being Tuple of (n + 1),W st (a,x) . W = p holds
Phi x = W . (a,(*' (a,p)))
let a be Point of RAS; for p being Tuple of (n + 1),RAS
for W being ATLAS of RAS
for x being Tuple of (n + 1),W st (a,x) . W = p holds
Phi x = W . (a,(*' (a,p)))
let p be Tuple of (n + 1),RAS; for W being ATLAS of RAS
for x being Tuple of (n + 1),W st (a,x) . W = p holds
Phi x = W . (a,(*' (a,p)))
let W be ATLAS of RAS; for x being Tuple of (n + 1),W st (a,x) . W = p holds
Phi x = W . (a,(*' (a,p)))
let x be Tuple of (n + 1),W; ( (a,x) . W = p implies Phi x = W . (a,(*' (a,p))) )
assume
(a,x) . W = p
; Phi x = W . (a,(*' (a,p)))
then
W . (a,p) = x
by Th15;
hence
Phi x = W . (a,(*' (a,p)))
by Lm4; verum