let T be InsType of SCM-Instr; :: thesis: ( T = 0 implies JumpParts T = {0} )
assume A1: T = 0 ; :: thesis: JumpParts T = {0}

hereby :: according to TARSKI:def 3,XBOOLE_0:def 10 :: thesis: {0} c= JumpParts T

let a be set ; :: thesis: ( a in JumpParts T implies a in {0} )
assume a in JumpParts T ; :: thesis: a in {0}
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 = 0 by A2, RECDEF_2:def 2;
hence a in {0} by TARSKI:def 1; :: thesis: verum

end;

let a be set ; :: according to TARSKI:def 3 :: thesis: ( not a in {0} or a in JumpParts T )
assume a in {0} ; :: thesis: a in JumpParts T
then A4: a = 0 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