End REDUCE.
(** The numberings associated to each instruction by the static analysis are inductively satisfiable, in the following sense: the numbering at the function entry point is satisfiable, and for any RTL execution from [pc] to [pc'], satisfiability at [pc] implies satisfiability at [pc']. *)

Theorem analysis_correct_entry:
forall ge sp rs m f vapprox approx,
analyze f vapprox = Some approx ->
exists valu, numbering_holds valu ge sp rs m approx!!(f.(fn_entrypoint)).