let s be State of SCM+FSA; :: thesis: for I being parahalting Program of SCM+FSA st I +* (Start-At (0,SCM+FSA)) c= s holds
ProgramPart s halts_on s
let I be parahalting Program of SCM+FSA; :: thesis: ( I +* (Start-At (0,SCM+FSA)) c= s implies ProgramPart s halts_on s )
assume A1: I +* (Start-At (0,SCM+FSA)) c= s ; :: thesis: ProgramPart s halts_on s
I +* (Start-At (0,SCM+FSA)) is halting by Def3;
hence ProgramPart s halts_on s by A1, EXTPRO_1:def 10; :: thesis: verum