let T be InsType of SCM-Instr; :: thesis: ( T = 0 implies JumpParts T = {{}} )

assume A1: T = 0 ; :: thesis: JumpParts T = {{}}

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

then A4: a = {} by TARSKI:def 1;

A5: JumpPart [SCM-Halt,{},{}] = {} ;

A6: InsCode [SCM-Halt,{},{}] = SCM-Halt ;

[SCM-Halt,{},{}] in SCM-Instr by Th1;

hence a in JumpParts T by A1, A4, A5, A6; :: thesis: verum

assume A1: T = 0 ; :: thesis: JumpParts T = {{}}

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

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

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

then consider I being Element of SCM-Instr such that

A2: a = JumpPart I and

A3: InsCode I = T ;

I in {[SCM-Halt,{},{}]} by A1, A3, Th9;

then I = [SCM-Halt,{},{}] by TARSKI:def 1;

then a = {} by A2;

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

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

then consider I being Element of SCM-Instr such that

A2: a = JumpPart I and

A3: InsCode I = T ;

I in {[SCM-Halt,{},{}]} by A1, A3, Th9;

then I = [SCM-Halt,{},{}] by TARSKI:def 1;

then a = {} by A2;

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

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

then A4: a = {} by TARSKI:def 1;

A5: JumpPart [SCM-Halt,{},{}] = {} ;

A6: InsCode [SCM-Halt,{},{}] = SCM-Halt ;

[SCM-Halt,{},{}] in SCM-Instr by Th1;

hence a in JumpParts T by A1, A4, A5, A6; :: thesis: verum