let s be State of SCM+FSA ; :: thesis: for I being parahalting Program of SCM+FSA st Initialized I c= s holds
s is halting
let I be parahalting Program of SCM+FSA ; :: thesis: ( Initialized I c= s implies s is halting )
A1: I +* (Start-At (insloc 0 )) is halting by Def3;
( Start-At (insloc 0 ) c= Initialized I & I c= Initialized I ) by FUNCT_4:26, SCMFSA6A:26;
then ( I +* (Start-At (insloc 0 )) c= I \/ (Start-At (insloc 0 )) & I \/ (Start-At (insloc 0 )) c= Initialized I ) by FUNCT_4:30, XBOOLE_1:8;
then A2: I +* (Start-At (insloc 0 )) c= Initialized I by XBOOLE_1:1;
assume Initialized I c= s ; :: thesis: s is halting
then I +* (Start-At (insloc 0 )) c= s by A2, XBOOLE_1:1;
hence s is halting by A1, AMI_1:def 26; :: thesis: verum