reserve l, m, n for Nat;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;

theorem
 for p being PartState of SCM+FSA holds
   (Initialized p).intloc 0 = 1
proof
 let p be PartState of SCM+FSA;
A1: ((intloc 0) .--> 1).intloc 0 = 1 by FUNCOP_1:72;
A2: Initialized p = Initialize(p +* ((intloc 0) .--> 1)) by FUNCT_4:14;
A3: intloc 0 in dom ((intloc 0) .--> 1) by TARSKI:def 1;
  not intloc 0 in dom SA0 by SCMFSA_2:102;
  hence (Initialized p).intloc 0 = (p+*((intloc 0) .--> 1)).intloc 0
         by A2,FUNCT_4:11
    .= 1 by A3,A1,FUNCT_4:13;
 end;
