let V be non empty addLoopStr ; :: thesis: for A, B being Subset of V
for l being C_Linear_Combination of A st A c= B holds
l is C_Linear_Combination of B
let A, B be Subset of V; :: thesis: for l being C_Linear_Combination of A st A c= B holds
l is C_Linear_Combination of B
let l be C_Linear_Combination of A; :: thesis: ( A c= B implies l is C_Linear_Combination of B )
assume A1: A c= B ; :: thesis: l is C_Linear_Combination of B
Carrier l c= A by Def4;
then Carrier l c= B by A1;
hence l is C_Linear_Combination of B by Def4; :: thesis: verum