let s be State of SCM+FSA; :: thesis: ( s . (intloc 0) = 1 & IC s = 0 implies Initialized s = s )
assume A1: s . (intloc 0) = 1 ; :: thesis: ( not IC s = 0 or Initialized s = s )
assume A2: IC s = 0 ; :: thesis: Initialized s = s
A3: IC SCM+FSA in dom s by COMPOS_1:9;
A4: intloc 0 in dom s by SCMFSA_2:66;
thus Initialized s = (s +* ((intloc 0) .--> 1)) +* (Start-At (0,SCM+FSA))
.= s +* ((IC SCM+FSA) .--> 0) by A1, A4, FUNCT_7:111
.= s by A2, A3, FUNCT_7:111 ; :: thesis: verum