let N be with_zero set ; :: thesis: for A being non empty with_non-empty_values IC-Ins-separated AMI-Struct over N
for I being Instruction of A st ex s being State of A st (Exec (I,s)) . (IC ) <> IC s holds
IC in Out_U_Inp I
let A be non empty with_non-empty_values IC-Ins-separated AMI-Struct over N; :: thesis: for I being Instruction of A st ex s being State of A st (Exec (I,s)) . (IC ) <> IC s holds
IC in Out_U_Inp I
let I be Instruction of A; :: thesis: ( ex s being State of A st (Exec (I,s)) . (IC ) <> IC s implies IC in Out_U_Inp I )
assume ex s being State of A st (Exec (I,s)) . (IC ) <> IC s ; :: thesis: IC in Out_U_Inp I
then A1: IC in Output I by Def3;
Output I c= Out_U_Inp I by Th4;
hence IC in Out_U_Inp I by A1; :: thesis: verum