let i be Instruction of SCM+FSA ; :: thesis: ( (Macro i) . 0 = i & (Macro i) . 1 = halt SCM+FSA & (Initialized (Macro i)) . 0 = i & (Initialized (Macro i)) . 1 = halt SCM+FSA & ((Macro i) +* (Start-At 0 ,SCM+FSA )) . 0 = i )
thus A1: (Macro i) . 0 = i by FUNCT_4:66; :: thesis: ( (Macro i) . 1 = halt SCM+FSA & (Initialized (Macro i)) . 0 = i & (Initialized (Macro i)) . 1 = halt SCM+FSA & ((Macro i) +* (Start-At 0 ,SCM+FSA )) . 0 = i )
thus A2: (Macro i) . 1 = halt SCM+FSA by FUNCT_4:66; :: thesis: ( (Initialized (Macro i)) . 0 = i & (Initialized (Macro i)) . 1 = halt SCM+FSA & ((Macro i) +* (Start-At 0 ,SCM+FSA )) . 0 = i )
A3: Macro i c= Initialized (Macro i) by SCMFSA6A:26;
A4: 0 in dom (Macro i) by Th32;
hence (Initialized (Macro i)) . 0 = i by A1, A3, GRFUNC_1:8; :: thesis: ( (Initialized (Macro i)) . 1 = halt SCM+FSA & ((Macro i) +* (Start-At 0 ,SCM+FSA )) . 0 = i )
1 in dom (Macro i) by Th32;
hence (Initialized (Macro i)) . 1 = halt SCM+FSA by A2, A3, GRFUNC_1:8; :: thesis: ((Macro i) +* (Start-At 0 ,SCM+FSA )) . 0 = i
dom (Macro i) misses dom (Start-At 0 ,SCM+FSA ) by SF_MASTR:64;
then Macro i c= (Macro i) +* (Start-At 0 ,SCM+FSA ) by FUNCT_4:33;
hence ((Macro i) +* (Start-At 0 ,SCM+FSA )) . 0 = i by A1, A4, GRFUNC_1:8; :: thesis: verum