let n be Element of NAT ; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: ( a,x . W = p implies Phi x = W . a,(*' a,p) )
assume a,x . W = p ; :: thesis: Phi x = W . a,(*' a,p)
then W . a,p = x by Th17;
hence Phi x = W . a,(*' a,p) by Lm4; :: thesis: verum