set Ma = Macro (b := (f,a));
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 (b := (f,a)) c= b₁ or b₁ halts_on s ) )
assume A56: Start-At (0,SCM+FSA) c= s ; :: thesis: for b₁ being set holds
( not Macro (b := (f,a)) c= b₁ or b₁ halts_on s )
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( not Macro (b := (f,a)) c= P or P halts_on s )
assume A57: Macro (b := (f,a)) c= P ; :: thesis: P halts_on s
A58: Macro (b := (f,a)) c= P by A57;
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 )
A59: dom P = NAT by PARTFUN1:def 4;
thus IC (Comput (P,s,1)) in dom P by A59; :: thesis: CurInstr (P,(Comput (P,s,1))) = halt SCM+FSA
dom (Start-At (0,SCM+FSA)) = {(IC )} by FUNCOP_1:19;
then A60: IC in dom (Start-At (0,SCM+FSA)) by TARSKI:def 1;
A61: IC s = (Start-At (0,SCM+FSA)) . (IC ) by A60, GRFUNC_1:8, A56
.= 0 by FUNCOP_1:87 ;
then A62: IC (Exec ((b := (f,a)),s)) = succ 0 by SCMFSA_2:98
.= 0 + 1 ;
A63: 1 in dom (Macro (b := (f,a))) by COMPOS_1:147;
A64: 0 in dom (Macro (b := (f,a))) by COMPOS_1:147;
A65: P . 0 = (Macro (b := (f,a))) . 0 by A58, A64, GRFUNC_1:8
.= b := (f,a) by COMPOS_1:148 ;
A66: P . 1 = (Macro (b := (f,a))) . 1 by A58, A63, 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 ((b := (f,a)),s) by A61, A59, PARTFUN1:def 8, A65 ;
hence CurInstr (P,(Comput (P,s,1))) = halt SCM+FSA by A62, A59, PARTFUN1:def 8, A66; :: thesis: verum