let s1, s2 be State of S; :: thesis: ( ex k being Nat st

( s1 = Comput (p,s,k) & CurInstr (p,s1) = halt S ) & ex k being Nat st

( s2 = Comput (p,s,k) & CurInstr (p,s2) = halt S ) implies s1 = s2 )

given k1 being Nat such that A2: ( s1 = Comput (p,s,k1) & CurInstr (p,s1) = halt S ) ; :: thesis: ( for k being Nat holds

( not s2 = Comput (p,s,k) or not CurInstr (p,s2) = halt S ) or s1 = s2 )

given k2 being 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, Th5; :: thesis: verum

( s1 = Comput (p,s,k) & CurInstr (p,s1) = halt S ) & ex k being Nat st

( s2 = Comput (p,s,k) & CurInstr (p,s2) = halt S ) implies s1 = s2 )

given k1 being Nat such that A2: ( s1 = Comput (p,s,k1) & CurInstr (p,s1) = halt S ) ; :: thesis: ( for k being Nat holds

( not s2 = Comput (p,s,k) or not CurInstr (p,s2) = halt S ) or s1 = s2 )

given k2 being 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, Th5; :: thesis: verum