reconsider f = the carrier of V --> zz as Element of Funcs ( the carrier of V,REAL) by FUNCT_2:8;

take f ; :: thesis: ex T being finite Subset of V st

for v being Element of V st not v in T holds

f . v = 0

take {} V ; :: thesis: for v being Element of V st not v in {} V holds

f . v = 0

thus for v being Element of V st not v in {} V holds

f . v = 0 by FUNCOP_1:7; :: thesis: verum

take f ; :: thesis: ex T being finite Subset of V st

for v being Element of V st not v in T holds

f . v = 0

take {} V ; :: thesis: for v being Element of V st not v in {} V holds

f . v = 0

thus for v being Element of V st not v in {} V holds

f . v = 0 by FUNCOP_1:7; :: thesis: verum