let n be 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 Th15;

hence Phi x = W . (a,(*' (a,p))) by Lm4; :: thesis: verum

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 Th15;

hence Phi x = W . (a,(*' (a,p))) by Lm4; :: thesis: verum