let N be with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite standard AMI-Struct of NAT ,N
for F being non empty programmed lower FinPartState of S holds FirstLoc F = il. S,0
let S be non empty stored-program IC-Ins-separated definite standard AMI-Struct of NAT ,N; :: thesis: for F being non empty programmed lower FinPartState of S holds FirstLoc F = il. S,0
let F be non empty programmed lower FinPartState of S; :: thesis: FirstLoc F = il. S,0
consider M being non empty Subset of NAT such that
M = { (locnum l) where l is Instruction-Location of S : l in dom F } and
A1: FirstLoc F = il. S,(min M) by Def2;
A2: FirstLoc F in dom F by Th21;
A3: il. S,0 <= il. S,(min M) by AMISTD_1:28;
then il. S,0 in dom F by A1, A2, AMISTD_1:def 20;
then FirstLoc F <= il. S,0 by Th23;
hence FirstLoc F = il. S,0 by A1, A3, AMISTD_1:def 9; :: thesis: verum