let i, j be Element of NAT ; :: thesis: for N being with_non-empty_elements set st i <= j holds
for S being non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N
for s being State of S st s halts_at IC (Computation s,i) holds
Computation s,j = Computation s,i
let N be with_non-empty_elements set ; :: thesis: ( i <= j implies for S being non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N
for s being State of S st s halts_at IC (Computation s,i) holds
Computation s,j = Computation s,i )
assume A1: i <= j ; :: thesis: for S being non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N
for s being State of S st s halts_at IC (Computation s,i) holds
Computation s,j = Computation s,i
let S be non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N; :: thesis: for s being State of S st s halts_at IC (Computation s,i) holds
Computation s,j = Computation s,i
let s be State of S; :: thesis: ( s halts_at IC (Computation s,i) implies Computation s,j = Computation s,i )
assume A2: s halts_at IC (Computation s,i) ; :: thesis: Computation s,j = Computation s,i
then s halts_at IC (Computation s,j) by A1, Th88;
hence Computation s,j = Result s by Th87
.= Computation s,i by A2, Th87 ;
:: thesis: verum