let I be Program of SCM+FSA; :: thesis: ( I is paraclosed implies I is InitClosed )
assume A1: I is paraclosed ; :: thesis: I is InitClosed
let s be State of SCM+FSA; :: according to SCM_HALT:def 1 :: thesis: for P being Instruction-Sequence of SCM+FSA st I c= P holds
for n being Element of NAT st Initialize ((intloc 0) .--> 1) c= s holds
IC (Comput (P,s,n)) in dom I
let P be Instruction-Sequence of SCM+FSA; :: thesis: ( I c= P implies for n being Element of NAT st Initialize ((intloc 0) .--> 1) c= s holds
IC (Comput (P,s,n)) in dom I )
assume A2: I c= P ; :: thesis: for n being Element of NAT st Initialize ((intloc 0) .--> 1) c= s holds
IC (Comput (P,s,n)) in dom I
let n be Element of NAT ; :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies IC (Comput (P,s,n)) in dom I )
assume A3: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: IC (Comput (P,s,n)) in dom I
Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:25;
then Start-At (0,SCM+FSA) c= s by A3, XBOOLE_1:1;
then s is 0 -started by MEMSTR_0:29;
hence IC (Comput (P,s,n)) in dom I by A1, A2, AMISTD_1:def 10; :: thesis: verum