let N be with_zero set ; :: thesis: for T being InsType of the InstructionsF of (STC N) holds JumpParts T = {0}
let T be InsType of the InstructionsF of (STC N); :: thesis: JumpParts T = {0}
set A = { (JumpPart I) where I is Instruction of (STC N) : InsCode I = T } ;
{0} = { (JumpPart I) where I is Instruction of (STC N) : InsCode I = T }

proof

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

let a be object ; :: thesis: ( a in {0} implies b₁ in { (JumpPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T } )
assume a in {0} ; :: thesis: b₁ in { (JumpPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T }
then A1: a = 0 by TARSKI:def 1;
A2: the InstructionsF of (STC N) = {[0,0,0],[1,0,0]} by AMISTD_1:def 7;
then A3: InsCodes the InstructionsF of (STC N) = {0,1} by MCART_1:91;

per cases ( T = 0 or T = 1 ) by A3, TARSKI:def 2;

suppose A4: T = 0 ; :: thesis: b₁ in { (JumpPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T }

reconsider I = [0,0,0] as Instruction of (STC N) by A2, TARSKI:def 2;
A5: JumpPart I = 0 ;
InsCode I = 0 ;
hence a in { (JumpPart I) where I is Instruction of (STC N) : InsCode I = T } by A1, A4, A5; :: thesis: verum

end;

suppose A6: T = 1 ; :: thesis: b₁ in { (JumpPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T }

reconsider I = [1,0,0] as Instruction of (STC N) by A2, TARSKI:def 2;
A7: JumpPart I = 0 ;
InsCode I = 1 ;
hence a in { (JumpPart I) where I is Instruction of (STC N) : InsCode I = T } by A1, A6, A7; :: thesis: verum

end;

end;

end;

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

end;

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