let s be State of SCM+FSA; :: thesis: for I, J being Program of SCM+FSA
for a being read-write Int-Location st s . a = 0 & I is_closed_onInit s & I is_halting_onInit s holds
IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA))
let I, J be Program of SCM+FSA; :: thesis: for a being read-write Int-Location st s . a = 0 & I is_closed_onInit s & I is_halting_onInit s holds
IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA))
let a be read-write Int-Location ; :: thesis: ( s . a = 0 & I is_closed_onInit s & I is_halting_onInit s implies IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA)) )
assume A1: s . a = 0 ; :: thesis: ( not I is_closed_onInit s or not I is_halting_onInit s or IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA)) )
set Is = Initialized s;
assume I is_closed_onInit s ; :: thesis: ( not I is_halting_onInit s or IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA)) )
then A2: I is_closed_on Initialized s by Th40;
assume I is_halting_onInit s ; :: thesis: IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA))
then I is_halting_on Initialized s by Th41;
hence IExec ((if=0 (a,I,J)),s) = (IExec (I,s)) +* (Start-At ((((card I) + (card J)) + 3),SCM+FSA)) by A1, A2, SCMFSA8B:17; :: thesis: verum