let N be non empty with_non-empty_elements set ; :: thesis: for T being InsType of (STC N) holds AddressParts T = {0 }
let T be InsType of (STC N); :: thesis: AddressParts T = {0 }
set A = { (AddressPart I) where I is Instruction of (STC N) : InsCode I = T } ;
{0 } = { (AddressPart I) where I is Instruction of (STC N) : InsCode I = T }

proof

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

let a be set ; :: thesis: ( a in {0 } implies b₁ in { (AddressPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T } )
assume a in {0 } ; :: thesis: b₁ in { (AddressPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T }
then A1: a = 0 by TARSKI:def 1;
A2: the Instructions of (STC N) = {[0 ,0 ],[1,0 ]} by AMISTD_1:def 11;
then A3: InsCodes (STC N) = {0 ,1} by RELAT_1:24;

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

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

reconsider I = [0 ,0 ] as Instruction of (STC N) by A2, TARSKI:def 2;
A5: AddressPart I = 0 by Th17;
InsCode I = 0 by MCART_1:def 1;
hence a in { (AddressPart 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 { (AddressPart b₂) where I is Instruction of (STC N) : InsCode b₂ = T }

reconsider I = [1,0 ] as Instruction of (STC N) by A2, TARSKI:def 2;
A7: AddressPart I = 0 by Th17;
InsCode I = 1 by MCART_1:def 1;
hence a in { (AddressPart I) where I is Instruction of (STC N) : InsCode I = T } by A1, A6, A7; :: thesis: verum

end;

end;

end;

let a be set ; :: according to TARSKI:def 3 :: thesis: ( not a in { (AddressPart I) where I is Instruction of (STC N) : InsCode I = T } or a in {0 } )
assume a in { (AddressPart 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 = AddressPart I & InsCode I = T ) ;
then a = 0 by Th17;
hence a in {0 } by TARSKI:def 1; :: thesis: verum

end;

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