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 I is halting holds
Out_U_Inp I is empty
let A be non empty with_non-empty_values IC-Ins-separated AMI-Struct over N; :: thesis: for I being Instruction of A st I is halting holds
Out_U_Inp I is empty
let I be Instruction of A; :: thesis: ( I is halting implies Out_U_Inp I is empty )
assume A1: for s being State of A holds Exec (I,s) = s ; :: according to EXTPRO_1:def 3 :: thesis: Out_U_Inp I is empty
assume not Out_U_Inp I is empty ; :: thesis: contradiction
then consider o being Object of A such that
A2: o in Out_U_Inp I ;
consider s being State of A, a being Element of Values o such that
A3: Exec (I,(s +* (o,a))) <> (Exec (I,s)) +* (o,a) by A2, Def5;
Exec (I,(s +* (o,a))) = s +* (o,a) by A1
.= (Exec (I,s)) +* (o,a) by A1 ;
hence contradiction by A3; :: thesis: verum