let I be Program of SCM+FSA; :: thesis: ( I is parahalting implies I is InitHalting )

assume A1: I is parahalting ; :: thesis: I is InitHalting

let s be State of SCM+FSA; :: according to SCM_HALT:def 1 :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for P being Instruction-Sequence of SCM+FSA st I c= P holds

P halts_on s )

assume A2: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for P being Instruction-Sequence of SCM+FSA st I c= P holds

P halts_on s

let P be Instruction-Sequence of SCM+FSA; :: thesis: ( I c= P implies P halts_on s )

assume A3: I c= P ; :: thesis: P halts_on s

Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:25;

then Start-At (0,SCM+FSA) c= s by A2, XBOOLE_1:1;

then s is 0 -started by MEMSTR_0:29;

hence P halts_on s by A1, A3, AMISTD_1:def 11; :: thesis: verum

assume A1: I is parahalting ; :: thesis: I is InitHalting

let s be State of SCM+FSA; :: according to SCM_HALT:def 1 :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for P being Instruction-Sequence of SCM+FSA st I c= P holds

P halts_on s )

assume A2: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for P being Instruction-Sequence of SCM+FSA st I c= P holds

P halts_on s

let P be Instruction-Sequence of SCM+FSA; :: thesis: ( I c= P implies P halts_on s )

assume A3: I c= P ; :: thesis: P halts_on s

Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:25;

then Start-At (0,SCM+FSA) c= s by A2, XBOOLE_1:1;

then s is 0 -started by MEMSTR_0:29;

hence P halts_on s by A1, A3, AMISTD_1:def 11; :: thesis: verum