let N be non empty with_non-empty_elements set ; :: thesis: for T being non empty stored-program IC-Ins-separated definite weakly_standard AMI-Struct of N
for F being NAT -defined non empty FinPartState of holds LastLoc F in dom F
let T be non empty stored-program IC-Ins-separated definite weakly_standard AMI-Struct of N; :: thesis: for F being NAT -defined non empty FinPartState of holds LastLoc F in dom F
let F be NAT -defined non empty FinPartState of ; :: thesis: LastLoc F in dom F
consider M being non empty finite natural-membered set such that
A1: M = { (locnum (l,T)) where l is Element of NAT : l in dom F } and
A2: LastLoc F = il. (T,(max M)) by Def21;
max M in M by XXREAL_2:def 8;
then ex l being Element of NAT st
( max M = locnum (l,T) & l in dom F ) by A1;
hence LastLoc F in dom F by A2, Def13; :: thesis: verum