let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite steady-programmed weakly_standard AMI-Struct of N
for F being NAT -defined the Instructions of b₁ -valued FinPartState of st F is really-closed & il. S,0 in dom F holds
F is para-closed
let S be non empty stored-program IC-Ins-separated definite steady-programmed weakly_standard AMI-Struct of N; :: thesis: for F being NAT -defined the Instructions of S -valued FinPartState of st F is really-closed & il. S,0 in dom F holds
F is para-closed
let F be NAT -defined the Instructions of S -valued FinPartState of ; :: thesis: ( F is really-closed & il. S,0 in dom F implies F is para-closed )
assume A1: ( ( for s being State of S st F c= s & IC s in dom F holds
for k being Element of NAT holds IC (Comput (ProgramPart s),s,k) in dom F ) & il. S,0 in dom F ) ; :: according to AMISTD_1:def 18 :: thesis: F is para-closed
let s be State of S; :: according to AMI_WSTD:def 19 :: thesis: ( F c= s & IC s = il. S,0 implies for k being Element of NAT holds IC (Comput (ProgramPart s),s,k) in dom F )
assume ( F c= s & IC s = il. S,0 ) ; :: thesis: for k being Element of NAT holds IC (Comput (ProgramPart s),s,k) in dom F
hence for k being Element of NAT holds IC (Comput (ProgramPart s),s,k) in dom F by A1; :: thesis: verum