consider F being PartFunc of C,the carrier of V such that
A3: for c being Element of C holds
( c in dom F iff S₁[c] ) and
A4: for c being Element of C st c in dom F holds
F /. c = H₂(c) from PARTFUN2:sch 2();
take F ; :: thesis: ( dom F = (dom f1) /\ (dom f2) & ( for c being Element of C st c in dom F holds
F /. c = (f1 /. c) - (f2 /. c) ) )
thus ( dom F = (dom f1) /\ (dom f2) & ( for c being Element of C st c in dom F holds
F /. c = (f1 /. c) - (f2 /. c) ) ) by A3, A4, SUBSET_1:8; :: thesis: verum