let T be InsType of SCM+FSA-Instr; :: thesis: ( ( T = 9 or T = 10 ) implies JumpParts T = {{}} )

assume A1: ( T = 9 or T = 10 ) ; :: thesis: JumpParts T = {{}}

then A2: not T = 0 & ... & not T = 8 ;

set f = the Element of SCM+FSA-Data*-Loc ;

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in {{}} or x in JumpParts T )

T in {9,10} by A1, TARSKI:def 2;

then A6: [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] in SCM+FSA-Instr by Th4;

assume x in {{}} ; :: thesis: x in JumpParts T

then x = {} by TARSKI:def 1;

then A7: x = JumpPart [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] ;

InsCode [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] = T ;

hence x in JumpParts T by A7, A6; :: thesis: verum

assume A1: ( T = 9 or T = 10 ) ; :: thesis: JumpParts T = {{}}

then A2: not T = 0 & ... & not T = 8 ;

hereby :: according to TARSKI:def 3,XBOOLE_0:def 10 :: thesis: {{}} c= JumpParts T

set a = the Element of SCM-Data-Loc ;let x be object ; :: thesis: ( x in JumpParts T implies x in {{}} )

assume x in JumpParts T ; :: thesis: x in {{}}

then consider I being Element of SCM+FSA-Instr such that

A3: x = JumpPart I and

A4: InsCode I = T ;

I in { [J,{},<*c,f,b*>] where J is Element of Segm 13, b, c is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} } by A1, A4, Th7, A2;

then consider J being Element of Segm 13, b, c being Element of SCM-Data-Loc , f being Element of SCM+FSA-Data*-Loc such that

A5: ( I = [J,{},<*c,f,b*>] & J in {9,10} ) ;

x = {} by A3, A5;

hence x in {{}} by TARSKI:def 1; :: thesis: verum

end;assume x in JumpParts T ; :: thesis: x in {{}}

then consider I being Element of SCM+FSA-Instr such that

A3: x = JumpPart I and

A4: InsCode I = T ;

I in { [J,{},<*c,f,b*>] where J is Element of Segm 13, b, c is Element of SCM-Data-Loc , f is Element of SCM+FSA-Data*-Loc : J in {9,10} } by A1, A4, Th7, A2;

then consider J being Element of Segm 13, b, c being Element of SCM-Data-Loc , f being Element of SCM+FSA-Data*-Loc such that

A5: ( I = [J,{},<*c,f,b*>] & J in {9,10} ) ;

x = {} by A3, A5;

hence x in {{}} by TARSKI:def 1; :: thesis: verum

set f = the Element of SCM+FSA-Data*-Loc ;

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in {{}} or x in JumpParts T )

T in {9,10} by A1, TARSKI:def 2;

then A6: [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] in SCM+FSA-Instr by Th4;

assume x in {{}} ; :: thesis: x in JumpParts T

then x = {} by TARSKI:def 1;

then A7: x = JumpPart [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] ;

InsCode [T,{},<* the Element of SCM-Data-Loc , the Element of SCM+FSA-Data*-Loc , the Element of SCM-Data-Loc *>] = T ;

hence x in JumpParts T by A7, A6; :: thesis: verum