let a1, a2 be Element of SCM+FSA-Data*-Loc ; :: thesis: ( ex c being Element of SCM+FSA-Data-Loc ex f being Element of SCM+FSA-Data*-Loc st
( <*c,f*> = x `2 & a1 = f ) & ex c being Element of SCM+FSA-Data-Loc ex f being Element of SCM+FSA-Data*-Loc st
( <*c,f*> = x `2 & a2 = f ) implies a1 = a2 )
given c1 being Element of SCM+FSA-Data-Loc , f1 being Element of SCM+FSA-Data*-Loc such that A6: <*c1,f1*> = x `2 and
A7: a1 = f1 ; :: thesis: ( for c being Element of SCM+FSA-Data-Loc
for f being Element of SCM+FSA-Data*-Loc holds
( not <*c,f*> = x `2 or not a2 = f ) or a1 = a2 )
given c2 being Element of SCM+FSA-Data-Loc , f2 being Element of SCM+FSA-Data*-Loc such that A8: <*c2,f2*> = x `2 and
A9: a2 = f2 ; :: thesis: a1 = a2
thus a1 = <*c1,f1*> /. 2 by A7, FINSEQ_4:26
.= a2 by A6, A8, A9, FINSEQ_4:26 ; :: thesis: verum