let S be non empty standard-ins homogeneous J/A-independent set ; :: thesis: for I being Element of S holds IncAddr (I,0) = I
let I be Element of S; :: thesis: IncAddr (I,0) = I
A1: InsCode (IncAddr (I,0)) = InsCode I by Def8;
A2: AddressPart (IncAddr (I,0)) = AddressPart I by Def8;
A3: JumpPart (IncAddr (I,0)) = 0 + (JumpPart I) by Def8;
then A4: dom (JumpPart I) = dom (JumpPart (IncAddr (I,0))) by VALUED_1:def 2;
for k being Nat st k in dom (JumpPart I) holds
(JumpPart (IncAddr (I,0))) . k = (JumpPart I) . k

proof

let k be Nat; :: thesis: ( k in dom (JumpPart I) implies (JumpPart (IncAddr (I,0))) . k = (JumpPart I) . k )
assume k in dom (JumpPart I) ; :: thesis: (JumpPart (IncAddr (I,0))) . k = (JumpPart I) . k
hence (JumpPart (IncAddr (I,0))) . k = 0 + ((JumpPart I) . k) by A4, A3, VALUED_1:def 2
.= (JumpPart I) . k ;
:: thesis: verum

end;

then JumpPart (IncAddr (I,0)) = JumpPart I by A4;
hence IncAddr (I,0) = I by A1, A2, Th1; :: thesis: verum