let N be non empty with_non-empty_elements set ; :: thesis: for A being non empty IC-Ins-separated standard AMI-Struct of N
for I being Instruction of A st I is sequential holds
not IC in Out_\_Inp I
let A be non empty IC-Ins-separated standard AMI-Struct of N; :: thesis: for I being Instruction of A st I is sequential holds
not IC in Out_\_Inp I
let I be Instruction of A; :: thesis: ( I is sequential implies not IC in Out_\_Inp I )
set t = the State of A;
set l = IC ;
reconsider sICt = succ (IC the State of A) as Element of NAT by ORDINAL1:def 12;
reconsider w = sICt as Element of ObjectKind (IC ) by MEMSTR_0:def 3;
set s = the State of A +* ((IC ),w);
assume for s being State of A holds (Exec (I,s)) . (IC ) = succ (IC s) ; :: according to AMISTD_1:def 8 :: thesis: not IC in Out_\_Inp I
then A1: ( (Exec (I, the State of A)) . (IC ) = succ (IC the State of A) & (Exec (I,( the State of A +* ((IC ),w)))) . (IC ) = succ (IC ( the State of A +* ((IC ),w))) ) ;
dom the State of A = the carrier of A by PARTFUN1:def 2;
then Exec (I, the State of A) <> Exec (I,( the State of A +* ((IC ),w))) by A1, FUNCT_7:31, ORDINAL1:9;
hence not IC in Out_\_Inp I by Def4; :: thesis: verum