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 realistic AMI-Struct of N
for F being PartFunc of (FinPartSt S),(FinPartSt S) st F = {} .--> {} holds
for p being pre-program of S holds p is Program of F
let S be non empty stored-program halting IC-Ins-separated steady-programmed definite realistic AMI-Struct of N; :: thesis: for F being PartFunc of (FinPartSt S),(FinPartSt S) st F = {} .--> {} holds
for p being pre-program of S holds p is Program of F
let F be PartFunc of (FinPartSt S),(FinPartSt S); :: thesis: ( F = {} .--> {} implies for p being pre-program of S holds p is Program of F )
assume A1: F = {} .--> {} ; :: thesis: for p being pre-program of S holds p is Program of F
let p be pre-program of S; :: thesis: p is Program of F
thus F is computable by A1, Th72; :: according to AMI_1:def 31 :: thesis: p computes F
thus p computes F by A1, Th70; :: thesis: verum