let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated steady-programmed definite realistic standard-ins standard without_implicit_jumps regular AMI-Struct of N
for I being Instruction of S st I is halting holds
I is IC-good
let S be non empty stored-program IC-Ins-separated steady-programmed definite realistic standard-ins standard without_implicit_jumps regular AMI-Struct of N; :: thesis: for I being Instruction of S st I is halting holds
I is IC-good
let I be Instruction of S; :: thesis: ( I is halting implies I is IC-good )
assume A1: I is halting ; :: thesis: I is IC-good
let k be natural number ; :: according to AMISTD_2:def 17 :: thesis: for s1, s2 being State of S st s2 = s1 +* ((IC S) .--> ((IC s1) + k,S)) holds
(IC (Exec I,s1)) + k,S = IC (Exec (IncAddr I,k),s2)
let s1, s2 be State of S; :: thesis: ( s2 = s1 +* ((IC S) .--> ((IC s1) + k,S)) implies (IC (Exec I,s1)) + k,S = IC (Exec (IncAddr I,k),s2) )
assume A2: s2 = s1 +* ((IC S) .--> ((IC s1) + k,S)) ; :: thesis: (IC (Exec I,s1)) + k,S = IC (Exec (IncAddr I,k),s2)
dom ((IC S) .--> ((IC s1) + k,S)) = {(IC S)} by FUNCOP_1:19;
then A3: IC S in dom ((IC S) .--> ((IC s1) + k,S)) by TARSKI:def 1;
thus (IC (Exec I,s1)) + k,S = (IC s1) + k,S by A1, AMI_1:def 8
.= ((IC S) .--> ((IC s1) + k,S)) . (IC S) by FUNCOP_1:87
.= IC s2 by A2, A3, FUNCT_4:14
.= IC (Exec I,s2) by A1, AMI_1:def 8
.= IC (Exec (IncAddr I,k),s2) by A1, Th29 ; :: thesis: verum