let I be Program of SCM+FSA; :: thesis: ( I is InitHalting iff for s being State of SCM+FSA
for p being Instruction-Sequence of SCM+FSA holds I is_halting_on Initialized s,p )

hereby :: thesis: ( ( for s being State of SCM+FSA
for p being Instruction-Sequence of SCM+FSA holds I is_halting_on Initialized s,p ) implies I is InitHalting )

assume A1: I is InitHalting ; :: thesis: for s being State of SCM+FSA
for p being Instruction-Sequence of SCM+FSA holds I is_halting_on Initialized s,p
let s be State of SCM+FSA; :: thesis: for p being Instruction-Sequence of SCM+FSA holds I is_halting_on Initialized s,p
let p be Instruction-Sequence of SCM+FSA; :: thesis: I is_halting_on Initialized s,p
I is_halting_onInit s,p by A1, Th36;
hence I is_halting_on Initialized s,p by Th41; :: thesis: verum

end;

assume A2: for s being State of SCM+FSA
for p being Instruction-Sequence of SCM+FSA holds I is_halting_on Initialized s,p ; :: thesis: I is InitHalting

now

let s be State of SCM+FSA; :: thesis: for p being Instruction-Sequence of SCM+FSA holds I is_halting_onInit s,p
let p be Instruction-Sequence of SCM+FSA; :: thesis: I is_halting_onInit s,p
I is_halting_on Initialized s,p by A2;
hence I is_halting_onInit s,p by Th41; :: thesis: verum

end;

hence I is InitHalting by Th36; :: thesis: verum