let s be State of ; :: thesis: for I being Program of st s . (intloc 0 ) = 1 & IC s = insloc 0 holds
s +* I = s +* (Initialized I)
let I be Program of ; :: thesis: ( s . (intloc 0 ) = 1 & IC s = insloc 0 implies s +* I = s +* (Initialized I) )
assume that
A1: s . (intloc 0 ) = 1 and
A2: IC s = insloc 0 ; :: thesis: s +* I = s +* (Initialized I)
A3: IC SCM+FSA in dom s by AMI_1:94;
thus s +* (Initialized I) = s +* (I +* (Start-At (insloc 0 ))) by A1, SCMFSA8C:18
.= (s +* I) +* (Start-At (insloc 0 )) by FUNCT_4:15
.= (s +* ((IC SCM+FSA ) .--> (insloc 0 ))) +* I by SCMFSA6B:14
.= s +* I by A2, A3, FUNCT_7:111 ; :: thesis: verum