let I, J be Program of SCM+FSA ; :: thesis: for a being read-write Int-Location
for s being State of SCM+FSA st s . a <= 0 & J is_closed_onInit s & J is_halting_onInit s holds
IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA )
let a be read-write Int-Location ; :: thesis: for s being State of SCM+FSA st s . a <= 0 & J is_closed_onInit s & J is_halting_onInit s holds
IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA )
let s be State of SCM+FSA ; :: thesis: ( s . a <= 0 & J is_closed_onInit s & J is_halting_onInit s implies IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA ) )
assume A1: s . a <= 0 ; :: thesis: ( not J is_closed_onInit s or not J is_halting_onInit s or IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA ) )
set Is = Initialized s;
assume J is_closed_onInit s ; :: thesis: ( not J is_halting_onInit s or IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA ) )
then A2: J is_closed_on Initialized s by Th40;
assume J is_halting_onInit s ; :: thesis: IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA )
then J is_halting_on Initialized s by Th41;
hence IExec (if>0 a,I,J),s = (IExec J,s) +* (Start-At (((card I) + (card J)) + 3),SCM+FSA ) by A1, A2, SCMFSA8B:25; :: thesis: verum