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(*              The Compcert verified compiler                         *)
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(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
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(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
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(** Correctness proof for operator strength reduction. *)
Local Transparent Archi.ptr64.
(** * Correctness of strength reduction *)
(** We now show that strength reduction over operators and addressing modes preserve semantics: the strength-reduced operations and addressings evaluate to the same values as the original ones if the actual arguments match the static approximations used for strength reduction. *)
Section STRENGTH_REDUCTION.
Variable bc: block_classification.
Variable ge: genv.
Hypothesis GENV: genv_match bc ge.
Variable sp: block.
Hypothesis STACK: bc sp = BCstack.
Variable ae: AE.t.
Variable rs: regset.
Variable m: mem.
Hypothesis MATCH: ematch bc rs ae.

Lemma match_S:
forall r ofs,
AE.get r ae = Ptr(Stk ofs) -> Val.lessdef rs#r (Vptr sp ofs).