let N be non empty with_non-empty_elements set ; :: thesis: for A being non empty stored-program IC-Ins-separated definite standard AMI-Struct of N
for I being Instruction of A st I is sequential holds
not IC A in Out_\_Inp I
let A be non empty stored-program IC-Ins-separated definite standard AMI-Struct of N; :: thesis: for I being Instruction of A st I is sequential holds
not IC A in Out_\_Inp I
let I be Instruction of A; :: thesis: ( I is sequential implies not IC A in Out_\_Inp I )
consider t being State of A;
set l = IC A;
reconsider w = NextLoc (IC t),A as Element of ObjectKind (IC A) by AMI_1:def 11;
set s = t +* (IC A),w;
assume for s being State of A holds (Exec I,s) . (IC A) = NextLoc (IC s),A ; :: according to AMISTD_1:def 16 :: thesis: not IC A in Out_\_Inp I
then A1: ( (Exec I,t) . (IC A) = NextLoc (IC t),A & (Exec I,(t +* (IC A),w)) . (IC A) = NextLoc (IC (t +* (IC A),w)),A ) ;
dom t = the carrier of A by PARTFUN1:def 4;
then Exec I,t <> Exec I,(t +* (IC A),w) by A1, AMISTD_1:35, FUNCT_7:33;
hence not IC A in Out_\_Inp I by Def4; :: thesis: verum