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_1:
forall ge sp rs m f vapprox approx pc pc' i,
analyze f vapprox = Some approx ->
f.(fn_code)!pc = Some i -> In pc' (successors_instr i) ->
(exists valu, numbering_holds valu ge sp rs m (transfer f vapprox pc approx!!pc)) ->
(exists valu, numbering_holds valu ge sp rs m approx!!pc').