defpred S₁[ object ] means $1 is Linear_Combination of V;
consider A being set such that
A1: for x being object holds
( x in A iff ( x in Funcs ( the carrier of V,REAL) & S₁[x] ) ) from XBOOLE_0:sch 1();
take A ; :: thesis: for x being set holds
( x in A iff x is Linear_Combination of V )
let x be set ; :: thesis: ( x in A iff x is Linear_Combination of V )
thus ( x in A implies x is Linear_Combination of V ) by A1; :: thesis: ( x is Linear_Combination of V implies x in A )
assume x is Linear_Combination of V ; :: thesis: x in A
hence x in A by A1; :: thesis: verum