consider k being Element of NAT such that
IC (Computation s,k) in dom (ProgramPart s) and
W: (ProgramPart s) . (IC (Computation s,k)) = halt S by A1, Def20;
(ProgramPart s) . (IC (Computation s,k)) = CurInstr (Computation s,k) by LmX;
hence ex b₁ being State of S ex k being Element of NAT st
( b₁ = Computation s,k & CurInstr b₁ = halt S ) by W; :: thesis: verum