Ltac TrivialExists :=
  match goal with
  | [ |- exists v2, Some ?v1 = Some v2 /\ Val.inject _ _ v2 ] =>
      exists v1; split; auto
  | _ => idtac
  end.

(* Specifications: *)
Lemma eval_operation_inj: forall op sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_operation op) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_operation ge1 sp1 op vl1 m1 = Some v1 -> exists v2, eval_operation ge2 sp2 op vl2 m2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_addressing_inj: forall addr sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_addressing addr) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_addressing ge1 sp1 addr vl1 = Some v1 -> exists v2, eval_addressing ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_addressing32_inj: forall addr sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_addressing addr) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_addressing32 ge1 sp1 addr vl1 = Some v1 -> exists v2, eval_addressing32 ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_addressing64_inj: forall addr sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_addressing addr) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_addressing64 ge1 sp1 addr vl1 = Some v1 -> exists v2, eval_addressing64 ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_addressing_inj: forall addr sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_addressing addr) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_addressing ge1 sp1 addr vl1 = Some v1 -> exists v2, eval_addressing ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_operation_inj: forall op sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_operation op) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_operation ge1 sp1 op vl1 m1 = Some v1 -> exists v2, eval_operation ge2 sp2 op vl2 m2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_operation_inj: forall op sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_operation op) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_operation ge1 sp1 op vl1 m1 = Some v1 -> exists v2, eval_operation ge2 sp2 op vl2 m2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_addressing_inj: forall addr sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_addressing addr) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_addressing ge1 sp1 addr vl1 = Some v1 -> exists v2, eval_addressing ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_operation_inj: forall op sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_operation op) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_operation ge1 sp1 op vl1 m1 = Some v1 -> exists v2, eval_operation ge2 sp2 op vl2 m2 = Some v2 /\ Val.inject f v1 v2.
Lemma eval_addressing_inj: forall addr sp1 vl1 sp2 vl2 v1, (forall id ofs, In id (globals_addressing addr) -> Val.inject f (Genv.symbol_address ge1 id ofs) (Genv.symbol_address ge2 id ofs)) -> Val.inject f sp1 sp2 -> Val.inject_list f vl1 vl2 -> eval_addressing ge1 sp1 addr vl1 = Some v1 -> exists v2, eval_addressing ge2 sp2 addr vl2 = Some v2 /\ Val.inject f v1 v2.