let x be Element of SCM+FSA-Instr ; :: thesis: ( ( x in SCM-Instr & ( InsCode x = 0 or InsCode x = 1 or InsCode x = 2 or InsCode x = 3 or InsCode x = 4 or InsCode x = 5 or InsCode x = 6 or InsCode x = 7 or InsCode x = 8 ) ) or ( x in { [J,{},<*c,f,b*>] where J is Element of Segm 13, c, b is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} } & ( InsCode x = 9 or InsCode x = 10 ) ) or ( x 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} } & ( InsCode x = 11 or InsCode x = 12 ) ) )
( x in SCM-Instr \/ { [J,{},<*c,f,b*>] where J is Element of Segm 13, c, b is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} } or x 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 XBOOLE_0:def 3;

per cases then ( x in SCM-Instr or x in { [J,{},<*c,f,b*>] where J is Element of Segm 13, c, b is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} } or x 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 XBOOLE_0:def 3;

case x in SCM-Instr ; :: thesis: ( InsCode x = 0 or InsCode x = 1 or InsCode x = 2 or InsCode x = 3 or InsCode x = 4 or InsCode x = 5 or InsCode x = 6 or InsCode x = 7 or InsCode x = 8 )

then InsCode x <= 8 by SCM_INST:10;
hence ( InsCode x = 0 or InsCode x = 1 or InsCode x = 2 or InsCode x = 3 or InsCode x = 4 or InsCode x = 5 or InsCode x = 6 or InsCode x = 7 or InsCode x = 8 ) by NAT_1:32; :: thesis: verum

end;

case x in { [J,{},<*c,f,b*>] where J is Element of Segm 13, c, b is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} } ; :: thesis: ( InsCode x = 9 or InsCode x = 10 )

then consider J being Element of Segm 13, c, b being Element of SCM-Data-Loc , f being Element of SCM+FSA-Data*-Loc such that
A1: x = [J,{},<*c,f,b*>] and
A2: J in {9,10} ;
InsCode x = J by A1, RECDEF_2:def 1;
hence ( InsCode x = 9 or InsCode x = 10 ) by A2, TARSKI:def 2; :: thesis: verum

end;

case x 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} } ; :: thesis: ( InsCode x = 11 or InsCode x = 12 )

then consider K being Element of Segm 13, c1 being Element of SCM-Data-Loc , f1 being Element of SCM+FSA-Data*-Loc such that
A3: x = [K,{},<*c1,f1*>] and
A4: K in {11,12} ;
InsCode x = K by A3, RECDEF_2:def 1;
hence ( InsCode x = 11 or InsCode x = 12 ) by A4, TARSKI:def 2; :: thesis: verum

end;

end;