let n be Element of NAT ; :: thesis: for RAS being ReperAlgebra of n
for a, b being Point of RAS
for p being Tuple of (n + 1),RAS
for W being ATLAS of RAS
for v being Vector of W
for x being Tuple of (n + 1),W st a,x . W = p & a,v . W = b & *' a,p = b holds
Phi x = v
let RAS be ReperAlgebra of n; :: thesis: for a, b being Point of RAS
for p being Tuple of (n + 1),RAS
for W being ATLAS of RAS
for v being Vector of W
for x being Tuple of (n + 1),W st a,x . W = p & a,v . W = b & *' a,p = b holds
Phi x = v
let a, b be Point of RAS; :: thesis: for p being Tuple of (n + 1),RAS
for W being ATLAS of RAS
for v being Vector of W
for x being Tuple of (n + 1),W st a,x . W = p & a,v . W = b & *' a,p = b holds
Phi x = v
let p be Tuple of (n + 1),RAS; :: thesis: for W being ATLAS of RAS
for v being Vector of W
for x being Tuple of (n + 1),W st a,x . W = p & a,v . W = b & *' a,p = b holds
Phi x = v
let W be ATLAS of RAS; :: thesis: for v being Vector of W
for x being Tuple of (n + 1),W st a,x . W = p & a,v . W = b & *' a,p = b holds
Phi x = v
let v be Vector of W; :: thesis: for x being Tuple of (n + 1),W st a,x . W = p & a,v . W = b & *' a,p = b holds
Phi x = v
let x be Tuple of (n + 1),W; :: thesis: ( a,x . W = p & a,v . W = b & *' a,p = b implies Phi x = v )
assume ( a,x . W = p & a,v . W = b & *' a,p = b ) ; :: thesis: Phi x = v
then Phi a,x = v by MIDSP_2:39;
hence Phi x = v by Def15; :: thesis: verum