let T be InsType of SCM-Instr; :: thesis: ( not not T = 1 & ... & not T = 5 implies JumpParts T = {{}} )

assume A1: not not T = 1 & ... & not T = 5 ; :: thesis: JumpParts T = {{}}

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

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

then A5: x = {} by TARSKI:def 1;

A6: JumpPart [T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] = {} ;

A7: InsCode [T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] = T ;

T in {1,2,3,4,5} by A1, ENUMSET1:def 3;

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

hence x in JumpParts T by A5, A6, A7; :: thesis: verum

assume A1: not not T = 1 & ... & not T = 5 ; :: thesis: JumpParts T = {{}}

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-Instr such that

A2: x = JumpPart I and

A3: InsCode I = T ;

I in { [J,{},<*b,c*>] where J is Element of Segm 9, b, c is Element of SCM-Data-Loc : J in {1,2,3,4,5} } by A1, A3, Th9;

then consider J being Element of Segm 9, b, c being Element of SCM-Data-Loc such that

A4: I = [J,{},<*b,c*>] and

J in {1,2,3,4,5} ;

x = {} by A2, A4;

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-Instr such that

A2: x = JumpPart I and

A3: InsCode I = T ;

I in { [J,{},<*b,c*>] where J is Element of Segm 9, b, c is Element of SCM-Data-Loc : J in {1,2,3,4,5} } by A1, A3, Th9;

then consider J being Element of Segm 9, b, c being Element of SCM-Data-Loc such that

A4: I = [J,{},<*b,c*>] and

J in {1,2,3,4,5} ;

x = {} by A2, A4;

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

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

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

then A5: x = {} by TARSKI:def 1;

A6: JumpPart [T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] = {} ;

A7: InsCode [T,{},<* the Element of SCM-Data-Loc , the Element of SCM-Data-Loc *>] = T ;

T in {1,2,3,4,5} by A1, ENUMSET1:def 3;

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

hence x in JumpParts T by A5, A6, A7; :: thesis: verum