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 ex b being Element of SCM+FSA-Data-Loc st
( <*c,f,b*> = x `2 & a1 = f ) & ex c being Element of SCM+FSA-Data-Loc ex f being Element of SCM+FSA-Data*-Loc ex b being Element of SCM+FSA-Data-Loc st
( <*c,f,b*> = x `2 & a2 = f ) implies a1 = a2 )
given c1 being Element of SCM+FSA-Data-Loc , f1 being Element of SCM+FSA-Data*-Loc , b1 being Element of SCM+FSA-Data-Loc such that A10: <*c1,f1,b1*> = x `2 and
A11: a1 = f1 ; :: thesis: ( for c being Element of SCM+FSA-Data-Loc
for f being Element of SCM+FSA-Data*-Loc
for b being Element of SCM+FSA-Data-Loc holds
( not <*c,f,b*> = 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 , b2 being Element of SCM+FSA-Data-Loc such that A12: <*c2,f2,b2*> = x `2 and
A13: a2 = f2 ; :: thesis: a1 = a2
thus a1 = <*c1,f1,b1*> /. 2 by A11, FINSEQ_4:27
.= a2 by A10, A12, A13, FINSEQ_4:27 ; :: thesis: verum