let x be set ; for c being Element of SCM-Data-Loc
for f being Element of SCM+FSA-Data*-Loc st x in {11,12} holds
[x,{},<*c,f*>] in SCM+FSA-Instr
let c be Element of SCM-Data-Loc ; for f being Element of SCM+FSA-Data*-Loc st x in {11,12} holds
[x,{},<*c,f*>] in SCM+FSA-Instr
let f be Element of SCM+FSA-Data*-Loc ; ( x in {11,12} implies [x,{},<*c,f*>] in SCM+FSA-Instr )
assume A1:
x in {11,12}
; [x,{},<*c,f*>] in SCM+FSA-Instr
then
( x = 11 or x = 12 )
by TARSKI:def 2;
then reconsider x = x as Element of Segm 13 by NAT_1:44;
[x,{},<*c,f*>] in { [K,{},<*c1,f1*>] where K is Element of Segm 13, c1 is Element of SCM-Data-Loc , f1 is Element of SCM+FSA-Data*-Loc : K in {11,12} }
by A1;
then
[x,{},<*c,f*>] in (SCM-Instr \/ { [J,{},<*c2,f2,b*>] where J is Element of Segm 13, b, c2 is Element of SCM-Data-Loc , f2 is Element of SCM+FSA-Data*-Loc : J in {9,10} } ) \/ { [K,{},<*c1,f1*>] where K is Element of Segm 13, c1 is Element of SCM-Data-Loc , f1 is Element of SCM+FSA-Data*-Loc : K in {11,12} }
by XBOOLE_0:def 3;
then
[x,{},<*c,f*>] in (SCM-Instr \/ { [J,{},<*c2,f2,b*>] where J is Element of Segm 13, b, c2 is Element of SCM-Data-Loc , f2 is Element of SCM+FSA-Data*-Loc : J in {9,10} } ) \/ { [K,{},<*c1,f1*>] where K is Element of Segm 13, c1 is Element of SCM-Data-Loc , f1 is Element of SCM+FSA-Data*-Loc : K in {11,12} }
;
hence
[x,{},<*c,f*>] in SCM+FSA-Instr
; verum