let s1, s2 be State of S; :: thesis: ( ex k being Element of NAT st
( s1 = Comput p,s,k & CurInstr p,s1 = halt S ) & ex k being Element of NAT st
( s2 = Comput p,s,k & CurInstr p,s2 = halt S ) implies s1 = s2 )
given k1 being Element of NAT such that A2: ( s1 = Comput p,s,k1 & CurInstr p,s1 = halt S ) ; :: thesis: ( for k being Element of NAT holds
( not s2 = Comput p,s,k or not CurInstr p,s2 = halt S ) or s1 = s2 )
given k2 being Element of NAT such that A3: ( s2 = Comput p,s,k2 & CurInstr p,s2 = halt S ) ; :: thesis: s1 = s2
( k1 <= k2 or k2 <= k1 ) ;
hence s1 = s2 by A2, A3, Th52; :: thesis: verum