set Mi = Macro (halt SCM+FSA);
let s be 0 -started State of SCM+FSA; :: according to SCMFSA6B:def 4 :: thesis: for b₁ being set holds
( not Macro (halt SCM+FSA) c= b₁ or for b₂ being Element of NAT holds (Comput (b₁,s,b₂)) . (intloc 0) = s . (intloc 0) )
A1: Start-At (0,SCM+FSA) c= s by MEMSTR_0:29;
let P be Instruction-Sequence of SCM+FSA; :: thesis: ( not Macro (halt SCM+FSA) c= P or for b₁ being Element of NAT holds (Comput (P,s,b₁)) . (intloc 0) = s . (intloc 0) )
assume A2: Macro (halt SCM+FSA) c= P ; :: thesis: for b₁ being Element of NAT holds (Comput (P,s,b₁)) . (intloc 0) = s . (intloc 0)
let k be Element of NAT ; :: thesis: (Comput (P,s,k)) . (intloc 0) = s . (intloc 0)
A3: s = Comput (P,s,0) by EXTPRO_1:2;
A4: P /. (IC s) = P . (IC s) by PBOOLE:143;
A5: 0 in dom (Macro (halt SCM+FSA)) by COMPOS_1:60;
Comput (P,s,0) = s by EXTPRO_1:2;
then CurInstr (P,(Comput (P,s,0))) = P . 0 by A1, A4, MEMSTR_0:39
.= (Macro (halt SCM+FSA)) . 0 by A2, A5, GRFUNC_1:2
.= halt SCM+FSA by COMPOS_1:58 ;
hence (Comput (P,s,k)) . (intloc 0) = s . (intloc 0) by A3, EXTPRO_1:5, NAT_1:2; :: thesis: verum