let x be Element of SCMPDS-Instr ; :: thesis: ( ( x in {[0,{},{}]} & InsCode x = 0 ) or ( x in { [14,{},<*l*>] where l is Element of INT : verum } & InsCode x = 14 ) or ( x in { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } & InsCode x = 1 ) or ( x in { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } & ( InsCode x = 2 or InsCode x = 3 ) ) or ( x in { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } & ( InsCode x = 4 or InsCode x = 5 or InsCode x = 6 or InsCode x = 7 or InsCode x = 8 ) ) or ( x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } & ( InsCode x = 9 or InsCode x = 10 or InsCode x = 11 or InsCode x = 12 or InsCode x = 13 ) ) )
( x in ((({[0,{},{}]} \/ { [14,{},<*l*>] where l is Element of INT : verum } ) \/ { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } ) \/ { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } ) \/ { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } or x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } ) by XBOOLE_0:def 3;
then ( x in (({[0,{},{}]} \/ { [14,{},<*l*>] where l is Element of INT : verum } ) \/ { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } ) \/ { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } or x in { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } or x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } ) by XBOOLE_0:def 3;
then ( x in ({[0,{},{}]} \/ { [14,{},<*l*>] where l is Element of INT : verum } ) \/ { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } or x in { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } or x in { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } or x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } ) by XBOOLE_0:def 3;
then ( x in {[0,{},{}]} \/ { [14,{},<*l*>] where l is Element of INT : verum } or x in { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } or x in { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } or x in { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } or x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } ) by XBOOLE_0:def 3;
per cases then ( x in {[0,{},{}]} or x in { [14,{},<*l*>] where l is Element of INT : verum } or x in { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } or x in { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } or x in { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } or x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } ) by XBOOLE_0:def 3;
case x in {[0,{},{}]} ; :: thesis: InsCode x = 0
then x = [0,{},{}] by TARSKI:def 1;
hence InsCode x = 0 ; :: thesis: verum
end;
case x in { [14,{},<*l*>] where l is Element of INT : verum } ; :: thesis: InsCode x = 14
then ex l being Element of INT st x = [14,{},<*l*>] ;
hence InsCode x = 14 ; :: thesis: verum
end;
case x in { [1,{},<*sp*>] where sp is Element of SCM-Data-Loc : verum } ; :: thesis: InsCode x = 1
then ex sp being Element of SCM-Data-Loc st x = [1,{},<*sp*>] ;
hence InsCode x = 1 ; :: thesis: verum
end;
case x in { [I,{},<*v,c*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c is Element of INT : I in {2,3} } ; :: thesis: ( InsCode x = 2 or InsCode x = 3 )
then consider I being Element of Segm 15, v being Element of SCM-Data-Loc , c being Element of INT such that
A1: x = [I,{},<*v,c*>] and
A2: I in {2,3} ;
InsCode x = I by A1;
hence ( InsCode x = 2 or InsCode x = 3 ) by A2, TARSKI:def 2; :: thesis: verum
end;
case x in { [I,{},<*v,c1,c2*>] where I is Element of Segm 15, v is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {4,5,6,7,8} } ; :: thesis: ( InsCode x = 4 or InsCode x = 5 or InsCode x = 6 or InsCode x = 7 or InsCode x = 8 )
then consider I being Element of Segm 15, v being Element of SCM-Data-Loc , c1, c2 being Element of INT such that
A3: x = [I,{},<*v,c1,c2*>] and
A4: I in {4,5,6,7,8} ;
InsCode x = I by A3;
hence ( InsCode x = 4 or InsCode x = 5 or InsCode x = 6 or InsCode x = 7 or InsCode x = 8 ) by A4, ENUMSET1:def 3; :: thesis: verum
end;
case x in { [I,{},<*v1,v2,c1,c2*>] where I is Element of Segm 15, v1, v2 is Element of SCM-Data-Loc , c1, c2 is Element of INT : I in {9,10,11,12,13} } ; :: thesis: ( InsCode x = 9 or InsCode x = 10 or InsCode x = 11 or InsCode x = 12 or InsCode x = 13 )
then consider I being Element of Segm 15, v1, v2 being Element of SCM-Data-Loc , c1, c2 being Element of INT such that
A5: x = [I,{},<*v1,v2,c1,c2*>] and
A6: I in {9,10,11,12,13} ;
InsCode x = I by A5;
hence ( InsCode x = 9 or InsCode x = 10 or InsCode x = 11 or InsCode x = 12 or InsCode x = 13 ) by A6, ENUMSET1:def 3; :: thesis: verum
end;
end;