let i, j be Nat; for N being non empty with_zero set st i <= j holds
for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for P being NAT -defined the InstructionsF of b2 -valued Function
for s being State of S st P halts_at IC (Comput (P,s,i)) holds
Comput (P,s,j) = Comput (P,s,i)
let N be non empty with_zero set ; ( i <= j implies for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for P being NAT -defined the InstructionsF of b1 -valued Function
for s being State of S st P halts_at IC (Comput (P,s,i)) holds
Comput (P,s,j) = Comput (P,s,i) )
assume A1:
i <= j
; for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for P being NAT -defined the InstructionsF of b1 -valued Function
for s being State of S st P halts_at IC (Comput (P,s,i)) holds
Comput (P,s,j) = Comput (P,s,i)
let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; for P being NAT -defined the InstructionsF of S -valued Function
for s being State of S st P halts_at IC (Comput (P,s,i)) holds
Comput (P,s,j) = Comput (P,s,i)
let P be NAT -defined the InstructionsF of S -valued Function; for s being State of S st P halts_at IC (Comput (P,s,i)) holds
Comput (P,s,j) = Comput (P,s,i)
let s be State of S; ( P halts_at IC (Comput (P,s,i)) implies Comput (P,s,j) = Comput (P,s,i) )
assume A2:
P halts_at IC (Comput (P,s,i))
; Comput (P,s,j) = Comput (P,s,i)
then
P halts_at IC (Comput (P,s,j))
by A1, Th19;
hence Comput (P,s,j) =
Result (P,s)
by Th18
.=
Comput (P,s,i)
by A2, Th18
;
verum