let R be Ring; :: thesis: for V being LeftMod of R
for A being Subset of V
for l being Linear_Combination of A
for X being Subset of V st X misses Carrier l & X <> {} holds
l .: X = {(0. R)}
let V be LeftMod of R; :: thesis: for A being Subset of V
for l being Linear_Combination of A
for X being Subset of V st X misses Carrier l & X <> {} holds
l .: X = {(0. R)}
let A be Subset of V; :: thesis: for l being Linear_Combination of A
for X being Subset of V st X misses Carrier l & X <> {} holds
l .: X = {(0. R)}
let l be Linear_Combination of A; :: thesis: for X being Subset of V st X misses Carrier l & X <> {} holds
l .: X = {(0. R)}
let X be Subset of V; :: thesis: ( X misses Carrier l & X <> {} implies l .: X = {(0. R)} )
assume that
A1: X misses Carrier l and
A2: X <> {} ; :: thesis: l .: X = {(0. R)}
dom l = [#] V by FUNCT_2:92;
hence l .: X = {(0. R)} by A1, A2, Th28, ZFMISC_1:33; :: thesis: verum