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 = Initialize 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 Initialize 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 Initialize 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