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