let T be InsType of the InstructionsF of Trivial-COM; :: thesis: JumpParts T = {0}
set A = { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T } ;
{0} = { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T }

proof

hereby :: according to TARSKI:def 3,XBOOLE_0:def 10 :: thesis: { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T } c= {0}

let a be object ; :: thesis: ( a in {0} implies a in { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T } )
assume a in {0} ; :: thesis: a in { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T }
then A1: a = 0 by TARSKI:def 1;
the InstructionsF of Trivial-COM = {[0,0,0]} by Def1;
then A2: InsCodes the InstructionsF of Trivial-COM = {0} by MCART_1:92;
A3: T = 0 by A2, TARSKI:def 1;
[0,0,0] = halt Trivial-COM ;
then reconsider I = [0,0,0] as Instruction of Trivial-COM ;
A4: JumpPart I = 0 ;
InsCode I = 0 ;
hence a in { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T } by A1, A3, A4; :: thesis: verum

end;

let a be object ; :: according to TARSKI:def 3 :: thesis: ( not a in { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T } or a in {0} )
assume a in { (JumpPart I) where I is Instruction of Trivial-COM : InsCode I = T } ; :: thesis: a in {0}
then ex I being Instruction of Trivial-COM st
( a = JumpPart I & InsCode I = T ) ;
then a = 0 by Th4;
hence a in {0} by TARSKI:def 1; :: thesis: verum

end;

hence JumpParts T = {0} ; :: thesis: verum