let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for s being State of S
for f being NAT -defined the Instructions of b₁ -valued finite Function
for k being Element of NAT st IC (Comput f,s,k) in dom f & f /. (IC (Comput f,s,k)) = halt S holds
Result f,s = Comput f,s,k
let S be non empty stored-program halting IC-Ins-separated definite AMI-Struct of N; :: thesis: for s being State of S
for f being NAT -defined the Instructions of S -valued finite Function
for k being Element of NAT st IC (Comput f,s,k) in dom f & f /. (IC (Comput f,s,k)) = halt S holds
Result f,s = Comput f,s,k
let s be State of S; :: thesis: for f being NAT -defined the Instructions of S -valued finite Function
for k being Element of NAT st IC (Comput f,s,k) in dom f & f /. (IC (Comput f,s,k)) = halt S holds
Result f,s = Comput f,s,k
let f be NAT -defined the Instructions of S -valued finite Function; :: thesis: for k being Element of NAT st IC (Comput f,s,k) in dom f & f /. (IC (Comput f,s,k)) = halt S holds
Result f,s = Comput f,s,k
let k be Element of NAT ; :: thesis: ( IC (Comput f,s,k) in dom f & f /. (IC (Comput f,s,k)) = halt S implies Result f,s = Comput f,s,k )
assume A1: IC (Comput f,s,k) in dom f ; :: thesis: ( not f /. (IC (Comput f,s,k)) = halt S or Result f,s = Comput f,s,k )
assume f /. (IC (Comput f,s,k)) = halt S ; :: thesis: Result f,s = Comput f,s,k
then A2: CurInstr f,(Comput f,s,k) = halt S ;
then f halts_on s by A1, Def8;
hence Result f,s = Comput f,s,k by A2, Def10; :: thesis: verum