let N be non empty with_non-empty_elements set ; :: 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 ex k being Element of NAT st s halts_at IC (Comput (ProgramPart s),s,k) holds
for i being Element of NAT holds Result s = Result (Comput (ProgramPart s),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 ex k being Element of NAT st s halts_at IC (Comput (ProgramPart s),s,k) holds
for i being Element of NAT holds Result s = Result (Comput (ProgramPart s),s,i)
let s be State of S; :: thesis: ( ex k being Element of NAT st s halts_at IC (Comput (ProgramPart s),s,k) implies for i being Element of NAT holds Result s = Result (Comput (ProgramPart s),s,i) )
given k being Element of NAT such that A1: s halts_at IC (Comput (ProgramPart s),s,k) ; :: thesis: for i being Element of NAT holds Result s = Result (Comput (ProgramPart s),s,i)
let i be Element of NAT ; :: thesis: Result s = Result (Comput (ProgramPart s),s,i)
s . (IC (Comput (ProgramPart s),s,k)) = halt S by A1, Def42;
hence Result s = Result (Comput (ProgramPart s),s,i) by Th57; :: thesis: verum