let I be Program of SCM+FSA; :: thesis: ( I is keeping_0 implies I is keepInt0_1 )
assume A43: I is keeping_0 ; :: thesis: I is keepInt0_1
let s be State of SCM+FSA; :: according to SCM_HALT:def 3 :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= p holds
for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A44: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= p holds
for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1
let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I c= p implies for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A45: I c= p ; :: thesis: for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1
let k be Element of NAT ; :: thesis: (Comput (p,s,k)) . (intloc 0) = 1
Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:26;
then B47: Start-At (0,SCM+FSA) c= s by A44, XBOOLE_1:1;
s . (intloc 0) = 1 by A44, Th7;
hence (Comput (p,s,k)) . (intloc 0) = 1 by A43, A45, B47, SCMFSA6B:def 4; :: thesis: verum