:: deftheorem Def4X defines (#) VSDIFF_1:def 1 :
for C being non empty set
for GF being Field
for V being VectSp of GF
for f being PartFunc of C,V
for r being Element of GF
for b₆ being PartFunc of C,V holds
( b₆ = r (#) f iff ( dom b₆ = dom f & ( for c being Element of C st c in dom b₆ holds
b₆ /. c = r * (f /. c) ) ) );