let I be Program of SCM+FSA; :: thesis: ( I is keeping_0 implies I is keepInt0_1 )
assume A1: I is keeping_0 ; :: thesis: I is keepInt0_1
let s be State of SCM+FSA; :: according to SCM_HALT:def 2 :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for p being Instruction-Sequence of SCM+FSA st I c= p holds
for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A2: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for p being Instruction-Sequence of SCM+FSA st I c= p holds
for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1
let p be Instruction-Sequence of SCM+FSA; :: thesis: ( I c= p implies for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A3: I c= p ; :: thesis: for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1
let k be Nat; :: thesis: (Comput (p,s,k)) . (intloc 0) = 1
Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:25;
then Start-At (0,SCM+FSA) c= s by A2, XBOOLE_1:1;
then A4: s is 0 -started by MEMSTR_0:29;
s . (intloc 0) = 1 by A2, SCMFSA_M:30;
hence (Comput (p,s,k)) . (intloc 0) = 1 by A1, A3, A4, SCMFSA6B:def 4; :: thesis: verum