set Ma = Macro (a :=len f);
let s be State of SCM+FSA; :: according to SCMFSA6B:def 3,SCMFSA6C:def 1 :: thesis: ( not Start-At (0,SCM+FSA) c= s or for b₁ being set holds
( not Macro (a :=len f) c= b₁ or b₁ halts_on s ) )
assume A1: Start-At (0,SCM+FSA) c= s ; :: thesis: for b₁ being set holds
( not Macro (a :=len f) c= b₁ or b₁ halts_on s )
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( not Macro (a :=len f) c= P or P halts_on s )
assume A2: Macro (a :=len f) c= P ; :: thesis: P halts_on s
A3: Macro (a :=len f) c= P by A2;
take 1 ; :: according to EXTPRO_1:def 7 :: thesis: ( IC (Comput (P,s,1)) in proj1 P & CurInstr (P,(Comput (P,s,1))) = halt SCM+FSA )
A4: dom P = NAT by PARTFUN1:def 4;
thus IC (Comput (P,s,1)) in dom P by A4; :: thesis: CurInstr (P,(Comput (P,s,1))) = halt SCM+FSA
dom (Start-At (0,SCM+FSA)) = {(IC )} by FUNCOP_1:19;
then A5: IC in dom (Start-At (0,SCM+FSA)) by TARSKI:def 1;
A6: IC s = (Start-At (0,SCM+FSA)) . (IC ) by A5, GRFUNC_1:8, A1
.= 0 by FUNCOP_1:87 ;
then A7: IC (Exec ((a :=len f),s)) = succ 0 by SCMFSA_2:100
.= 0 + 1 ;
A8: 1 in dom (Macro (a :=len f)) by COMPOS_1:147;
A9: 0 in dom (Macro (a :=len f)) by COMPOS_1:147;
A10: P . 0 = (Macro (a :=len f)) . 0 by A3, A9, GRFUNC_1:8
.= a :=len f by COMPOS_1:148 ;
A11: P . 1 = (Macro (a :=len f)) . 1 by A3, A8, GRFUNC_1:8
.= halt SCM+FSA by COMPOS_1:148 ;
Comput (P,s,(0 + 1)) = Following (P,(Comput (P,s,0))) by EXTPRO_1:4
.= Following (P,s) by EXTPRO_1:3
.= Exec ((a :=len f),s) by A6, A4, PARTFUN1:def 8, A10 ;
hence CurInstr (P,(Comput (P,s,1))) = halt SCM+FSA by A7, A4, PARTFUN1:def 8, A11; :: thesis: verum