let D be non empty set ; :: thesis: for p being Element of D
for f1, f2 being FinSequence of D st p in rng f1 holds
(f1 ^ f2) -: p = f1 -: p
let p be Element of D; :: thesis: for f1, f2 being FinSequence of D st p in rng f1 holds
(f1 ^ f2) -: p = f1 -: p
let f1, f2 be FinSequence of D; :: thesis: ( p in rng f1 implies (f1 ^ f2) -: p = f1 -: p )
assume A1: p in rng f1 ; :: thesis: (f1 ^ f2) -: p = f1 -: p
rng (f1 ^ f2) = (rng f1) \/ (rng f2) by FINSEQ_1:31;
then p in rng (f1 ^ f2) by A1, XBOOLE_0:def 3;
hence (f1 ^ f2) -: p = ((f1 ^ f2) -| p) ^ <*p*> by Th40
.= (f1 -| p) ^ <*p*> by A1, Th12
.= f1 -: p by A1, Th40 ;
:: thesis: verum