let AS be AffinSpace; :: thesis: for a being Element of AS
for A being Subset of AS st A is being_line holds
a * A is being_line
let a be Element of AS; :: thesis: for A being Subset of AS st A is being_line holds
a * A is being_line
let A be Subset of AS; :: thesis: ( A is being_line implies a * A is being_line )
set M = a * A;
assume A is being_line ; :: thesis: a * A is being_line
then A // a * A by Def3;
hence a * A is being_line by AFF_1:36; :: thesis: verum