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memory_cmp_impl_soundness.v
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Require Import Arith.
Require Import Nat.
Require Import Bool.
Require Import bbv.Word.
Require Import Coq.NArith.NArith.
Require Import List.
Import ListNotations.
Require Import FORVES2.constants.
Import Constants.
Require Import FORVES2.program.
Import Program.
Require Import FORVES2.execution_state.
Import ExecutionState.
Require Import FORVES2.stack_operation_instructions.
Import StackOpInstrs.
Require Import FORVES2.misc.
Import Misc.
Require Import FORVES2.symbolic_state.
Import SymbolicState.
Require Import FORVES2.symbolic_state_eval.
Import SymbolicStateEval.
Require Import FORVES2.symbolic_state_eval_facts.
Import SymbolicStateEvalFacts.
Require Import FORVES2.valid_symbolic_state.
Import ValidSymbolicState.
Require Import FORVES2.symbolic_state_cmp.
Import SymbolicStateCmp.
Require Import FORVES2.memory_cmp_impl.
Import MemoryCmpImpl.
Require Import FORVES2.eval_common.
Import EvalCommon.
Require Import FORVES2.concrete_interpreter.
Import ConcreteInterpreter.
Require Import Coq.Logic.FunctionalExtensionality.
Require Import FORVES2.memory_ops_solvers_impl_soundness.
Import MemoryOpsSolversImplSoundness.
Require Import FORVES2.constraints.
Import Constraints.
Require Import FORVES2.context.
Import Context.
Require Import FORVES2.context_facts.
Import ContextFacts.
Require Import FORVES2.symbolic_execution_soundness.
Import SymbolicExecutionSoundness.
Module MemoryCmpImplSoundness.
Theorem trivial_memory_cmp_snd:
safe_smemory_cmp_ext_wrt_sstack_value_cmp trivial_memory_cmp.
Proof.
unfold safe_smemory_cmp_ext_wrt_sstack_value_cmp.
unfold safe_sstack_val_cmp_ext_1_d.
unfold safe_smemory_cmp_ext_d.
unfold safe_smemory_cmp.
unfold trivial_memory_cmp.
intros.
destruct smem1; destruct smem2; try discriminate.
exists mem.
auto.
Qed.
Theorem basic_memory_cmp_snd:
safe_smemory_cmp_ext_wrt_sstack_value_cmp basic_memory_cmp.
Proof.
unfold safe_smemory_cmp_ext_wrt_sstack_value_cmp.
intros d sstack_val_cmp H_sstack_val_cmp_snd.
unfold safe_smemory_cmp_ext_d.
intros d' H_d'_le_d.
unfold safe_smemory_cmp.
intros ctx smem1 smem2 maxidx1 sb1 maxidx2 sb2 ops H_valid_sb1 H_valid_sb2.
revert smem2.
revert smem1.
induction smem1 as [|u1 smem1' IHsmem1'].
+ intros smem2 H_valid_smem1 H_valid_smem2 H_basic_mem_cmp model mem strg exts H_is_model.
destruct smem2; try discriminate.
exists mem.
unfold eval_smemory.
simpl.
split; reflexivity.
+ intros smem2 H_valid_smem1 H_valid_smem2 H_basic_mem_cmp model mem strg exts H_is_model.
destruct smem2 as [|u2 smem2'] eqn:H_smem2.
++ simpl in H_basic_mem_cmp.
destruct u1; try discriminate.
++ simpl in H_basic_mem_cmp.
destruct u1 as [soffset1 svalue1|soffset1 svalue1] eqn:E_u1; destruct u2 as [soffset2 svalue2|soffset2 svalue2] eqn:E_u2; try discriminate.
+++ destruct (sstack_val_cmp d' ctx soffset1 soffset2 maxidx1 sb1 maxidx2 sb2 ops) eqn:E_cmp_soffset1_soffset2; try discriminate.
destruct (sstack_val_cmp d' ctx svalue1 svalue2 maxidx1 sb1 maxidx2 sb2 ops) eqn:E_cmp_svalue1_svalue2; try discriminate.
simpl in H_valid_smem1.
destruct H_valid_smem1 as [ [H_valid_soffset1 H_valid_svalue1] H_valid_smem1'].
simpl in H_valid_smem2.
destruct H_valid_smem2 as [ [H_valid_soffset2 H_valid_svalue2] H_valid_smem2'].
pose proof (IHsmem1' smem2' H_valid_smem1' H_valid_smem2' H_basic_mem_cmp model mem strg exts H_is_model) as IHsmem1'_0.
destruct IHsmem1'_0 as [mem' [IHsmem1'_0 IHsmem1'_1]].
unfold safe_sstack_val_cmp_ext_1_d in H_sstack_val_cmp_snd.
pose proof (H_sstack_val_cmp_snd d' H_d'_le_d) as H_sstack_val_cmp_snd_d'.
unfold safe_sstack_val_cmp in H_sstack_val_cmp_snd_d'.
pose proof(H_sstack_val_cmp_snd_d' ctx soffset1 soffset2 maxidx1 sb1 maxidx2 sb2 ops H_valid_soffset1 H_valid_soffset2 H_valid_sb1 H_valid_sb2 E_cmp_soffset1_soffset2 model mem strg exts H_is_model) as H_eval_soffset1_soffset2.
destruct H_eval_soffset1_soffset2 as [soffset_1_2_v [H_eval_soffset1 H_eval_soffset2]].
pose proof(H_sstack_val_cmp_snd_d' ctx svalue1 svalue2 maxidx1 sb1 maxidx2 sb2 ops H_valid_svalue1 H_valid_svalue2 H_valid_sb1 H_valid_sb2 E_cmp_svalue1_svalue2 model mem strg exts H_is_model) as H_eval_svalue1_svalue2.
destruct H_eval_svalue1_svalue2 as [svalue_1_2_v [H_eval_svalue1 H_eval_svalue2]].
exists (mstore mem' svalue_1_2_v soffset_1_2_v).
unfold eval_smemory in IHsmem1'_0.
destruct (map_option (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx1 sb1 ops)) smem1') as [updates1|] eqn:H_mo_smem1'; try discriminate.
injection IHsmem1'_0 as IHsmem1'_0.
unfold eval_smemory in IHsmem1'_1.
destruct (map_option (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx2 sb2 ops)) smem2') as [updates2|] eqn:H_mo_smem2'; try discriminate.
injection IHsmem1'_1 as IHsmem1'_1.
unfold eval_smemory.
unfold map_option.
repeat rewrite <- map_option_ho.
unfold instantiate_memory_update at 1.
rewrite H_eval_soffset1.
rewrite H_eval_svalue1.
unfold instantiate_memory_update at 2.
rewrite H_eval_soffset2.
rewrite H_eval_svalue2.
rewrite H_mo_smem1'.
rewrite H_mo_smem2'.
unfold update_memory.
fold update_memory.
rewrite IHsmem1'_0.
rewrite IHsmem1'_1.
simpl.
split; reflexivity.
(* copy of previous item *)
+++ destruct (sstack_val_cmp d' ctx soffset1 soffset2 maxidx1 sb1 maxidx2 sb2 ops) eqn:E_cmp_soffset1_soffset2; try discriminate.
destruct (sstack_val_cmp d' ctx svalue1 svalue2 maxidx1 sb1 maxidx2 sb2 ops) eqn:E_cmp_svalue1_svalue2; try discriminate.
simpl in H_valid_smem1.
destruct H_valid_smem1 as [ [H_valid_soffset1 H_valid_svalue1] H_valid_smem1'].
simpl in H_valid_smem2.
destruct H_valid_smem2 as [ [H_valid_soffset2 H_valid_svalue2] H_valid_smem2'].
pose proof (IHsmem1' smem2' H_valid_smem1' H_valid_smem2' H_basic_mem_cmp model mem strg exts H_is_model) as IHsmem1'_0.
destruct IHsmem1'_0 as [mem' [IHsmem1'_0 IHsmem1'_1]].
unfold safe_sstack_val_cmp_ext_1_d in H_sstack_val_cmp_snd.
pose proof (H_sstack_val_cmp_snd d' H_d'_le_d) as H_sstack_val_cmp_snd_d'.
unfold safe_sstack_val_cmp in H_sstack_val_cmp_snd_d'.
pose proof(H_sstack_val_cmp_snd_d' ctx soffset1 soffset2 maxidx1 sb1 maxidx2 sb2 ops H_valid_soffset1 H_valid_soffset2 H_valid_sb1 H_valid_sb2 E_cmp_soffset1_soffset2 model mem strg exts H_is_model) as H_eval_soffset1_soffset2.
destruct H_eval_soffset1_soffset2 as [soffset_1_2_v [H_eval_soffset1 H_eval_soffset2]].
pose proof(H_sstack_val_cmp_snd_d' ctx svalue1 svalue2 maxidx1 sb1 maxidx2 sb2 ops H_valid_svalue1 H_valid_svalue2 H_valid_sb1 H_valid_sb2 E_cmp_svalue1_svalue2 model mem strg exts H_is_model) as H_eval_svalue1_svalue2.
destruct H_eval_svalue1_svalue2 as [svalue_1_2_v [H_eval_svalue1 H_eval_svalue2]].
exists (mstore mem' (split1_byte (svalue_1_2_v: word ((S (pred BytesInEVMWord))*8))) soffset_1_2_v).
unfold eval_smemory in IHsmem1'_0.
destruct (map_option (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx1 sb1 ops)) smem1') as [updates1|] eqn:H_mo_smem1'; try discriminate.
injection IHsmem1'_0 as IHsmem1'_0.
unfold eval_smemory in IHsmem1'_1.
destruct (map_option (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx2 sb2 ops)) smem2') as [updates2|] eqn:H_mo_smem2'; try discriminate.
injection IHsmem1'_1 as IHsmem1'_1.
unfold eval_smemory.
unfold map_option.
repeat rewrite <- map_option_ho.
unfold instantiate_memory_update at 1.
rewrite H_eval_soffset1.
rewrite H_eval_svalue1.
unfold instantiate_memory_update at 2.
rewrite H_eval_soffset2.
rewrite H_eval_svalue2.
rewrite H_mo_smem1'.
rewrite H_mo_smem2'.
unfold update_memory.
fold update_memory.
rewrite IHsmem1'_0.
rewrite IHsmem1'_1.
simpl.
split; reflexivity.
Qed.
Lemma reorder_updates'_valid:
forall ctx maxidx sb ops,
valid_bindings maxidx sb ops ->
forall d smem b smem_r,
valid_smemory maxidx smem ->
reorder_updates' d ctx smem maxidx sb = (b,smem_r) ->
valid_smemory maxidx smem_r.
Proof.
intros ctx maxidx sb ops H_valid_sb.
induction d as [|d'' IHd'].
+ intros smem b smem_r H_valid_smem H_reorder'.
simpl in H_reorder'.
injection H_reorder' as H_b H_smem_r.
rewrite <- H_smem_r.
apply H_valid_smem.
+ intros smem b smem_r H_valid_smem H_reorder'.
simpl in H_reorder'.
destruct smem as [|u1 smem'] eqn:H_smem.
++ injection H_reorder' as H_b H_smem_r.
rewrite <- H_smem_r.
simpl.
auto.
++ destruct smem' as [|u2 smem''] eqn:H_smem'.
+++ injection H_reorder' as H_b H_smem_r.
rewrite <- H_smem_r.
simpl.
split; try auto.
apply H_valid_smem.
+++ destruct (swap_memory_update ctx u1 u2 maxidx sb) eqn:E_swap.
++++ destruct (reorder_updates' d'' ctx (u1 :: smem'')) eqn:E_reorder'_rec.
injection H_reorder' as H_b H_smem_r.
rewrite <- H_smem_r.
simpl in H_valid_smem.
destruct H_valid_smem as [H_valid_u1 [H_valid_u2 H_valid_smem'']].
pose proof (IHd' (u1 :: smem'') b0 s (valid_smemory_when_extended_with_valid_update maxidx u1 smem'' H_valid_u1 H_valid_smem'') E_reorder'_rec) as IHd'_0.
simpl.
split.
+++++ apply H_valid_u2.
+++++ apply IHd'_0.
++++ destruct (reorder_updates' d'' ctx (u2 :: smem'')) eqn:E_reorder'_rec.
injection H_reorder' as H_b H_smem_r.
rewrite <- H_smem_r.
simpl in H_valid_smem.
destruct H_valid_smem as [H_valid_u1 [H_valid_u2 H_valid_smem'']].
pose proof (IHd' (u2 :: smem'') b0 s (valid_smemory_when_extended_with_valid_update maxidx u2 smem'' H_valid_u2 H_valid_smem'') E_reorder'_rec) as IHd'_0.
simpl.
split.
+++++ apply H_valid_u1.
+++++ apply IHd'_0.
Qed.
Lemma x_eq_offset_false_implied:
forall n offset1 offset2 x,
(offset1+(N.of_nat (S n)) <=? offset2)%N = true ->
(x =? offset1)%N = true ->
(x =? offset2)%N = false.
Proof.
intros n offset1 offset2 x H_no_overlap H_x_offset1.
simpl in H_no_overlap.
rewrite N.eqb_eq in H_x_offset1.
rewrite H_x_offset1.
rewrite N.eqb_neq.
apply N.lt_neq.
pose proof (N.leb_le (offset1 + N.pos (Pos.of_succ_nat n))%N offset2) as H_leb_le.
rewrite H_leb_le in H_no_overlap.
apply Nlt_in.
intuition.
Qed.
Lemma n_le_m_implies_n_lt_m_plus_1:
forall n m,
(n <=? m = true -> n <? m+1 = true)%N.
Proof.
intros n m H_n_le_m.
rewrite N.ltb_lt.
rewrite N.leb_le in H_n_le_m.
apply Nlt_in.
intuition.
Qed.
Lemma n_le_m_implies_n_le_m_plus_1:
forall n m,
(n <=? m = true -> n <=? m+1 = true)%N.
Proof.
intros n m H_n_le_m.
rewrite N.leb_le.
rewrite N.leb_le in H_n_le_m.
apply N.le_lteq.
left.
apply Nlt_in.
intuition.
Qed.
Lemma Nle_in:
forall n m : N, N.to_nat n <= N.to_nat m -> (n <= m)%N.
Proof.
intros n m H.
apply Nat.le_lteq in H.
destruct H.
+ apply Nlt_in in H.
apply N.le_lteq.
left.
apply H.
+ apply N.le_lteq.
right.
apply nat_of_N_eq in H.
apply H.
Qed.
Lemma n_lt_m_implies_n_plus_1_le_m:
forall n m,
(n <? m = true -> n+1 <=? m = true)%N.
Proof.
intros n m H_n_lt_m.
rewrite N.leb_le.
pose proof Nlt_in.
rewrite N.ltb_lt in H_n_lt_m.
apply Nlt_out in H_n_lt_m.
apply Nle_in.
intuition.
Qed.
Lemma update_same_address_mstore'_aux:
forall n m mem (value1: word (S n*8)) (value2: word (m*8)) offset1 offset2 x,
(offset1+(N.of_nat (S n)) <=? offset2)%N = true ->
(x =? offset1)%N = true ->
mstore'
(fun offset' : N =>
if (offset' =? offset1)%N
then split1_byte value1
else mstore' mem (split2_byte value1) (offset1 + 1) offset') value2 offset2
x = split1_byte value1.
Proof.
intros n m.
revert m n.
induction m as [|m'].
+ intros n mem value1 value2 offset1 offset2 x H_no_overlap H_x_eq_offset1.
simpl.
rewrite H_x_eq_offset1.
reflexivity.
+ intros n mem value1 value2 offset1 offset2 x H_no_overlap H_x_eq_offset1.
simpl.
assert(H_x_offset2: (x =? offset2)%N = false). apply (x_eq_offset_false_implied n offset1 offset2 x H_no_overlap H_x_eq_offset1).
assert(H_no_overlap': (offset1 + N.of_nat (S n) <=? offset2+1)%N = true).
apply (n_le_m_implies_n_le_m_plus_1 (offset1 + N.of_nat (S n))%N offset2 H_no_overlap).
rewrite H_x_offset2.
pose proof (IHm' n mem value1 (split2_byte value2) offset1 (offset2+1)%N x H_no_overlap' H_x_eq_offset1) as IHm'_0.
apply IHm'_0.
Qed.
Lemma update_same_address_mstore'_aux'':
forall n m mem (value1: word (S n*8)) (value2: word (m*8)) offset1 offset2 x,
(offset1+(N.of_nat (S n)) <=? offset2)%N = true ->
(x =? offset1)%N = false ->
mstore'
(fun offset' : N =>
if (offset' =? offset1)%N
then split1_byte value1
else mstore' mem (split2_byte value1) (offset1 + 1) offset') value2 offset2
x = mstore'
(mstore' mem (split2_byte value1) (offset1 + 1)) value2 offset2 x.
Proof.
intros n m.
revert m n.
induction m as [|m' IHm'].
+ intros n nmem value1 value2 offset1 offset2 x H_no_overlap H_x_offset1.
simpl.
rewrite H_x_offset1.
reflexivity.
+ intros n mem value1 value2 offset1 offset2 x H_no_overlap H_x_offset1.
simpl.
destruct (x =? offset2)%N eqn:E_x_offset2; try reflexivity.
assert(H_no_overlap': (offset1 + N.of_nat (S n) <=? offset2+1)%N = true).
apply (n_le_m_implies_n_le_m_plus_1 (offset1 + N.of_nat (S n))%N offset2 H_no_overlap).
pose proof (IHm' n mem value1 (split2_byte value2) offset1 (offset2+1)%N x H_no_overlap' H_x_offset1) as IHm'_0.
apply IHm'_0.
Qed.
Lemma mstore_non_overlap_updates:
forall n m mem offset1 (value1 : word (n*8)) offset2 (value2: word (m*8)),
(offset1+(N.of_nat n) <=? offset2)%N = true ->
mstore' (mstore' mem value1 offset1) value2 offset2 =
mstore' (mstore' mem value2 offset2) value1 offset1.
Proof.
induction n as [|n' IHn'].
+ intros m mem offset1 value1 offset2 value2 H_no_overlap.
unfold mstore' at 2.
unfold mstore' at 2.
reflexivity.
+ intros m mem offset1 value1 offset2 value2 H_no_overlap.
apply functional_extensionality.
intro x.
simpl.
destruct (x =? offset1)%N eqn:E_x_offset1.
++ rewrite update_same_address_mstore'_aux.
reflexivity.
apply H_no_overlap.
apply E_x_offset1.
++ rewrite update_same_address_mstore'_aux''.
assert (H_no_overlap': (offset1 + 1 + N.of_nat n' <=? offset2)%N = true). rewrite <- N_x_nat_of_Si. apply H_no_overlap.
pose proof (IHn' m mem (offset1 + 1)%N (split2_byte value1) offset2 value2 H_no_overlap') as IHn'_0.
rewrite IHn'_0.
reflexivity.
apply H_no_overlap.
apply E_x_offset1.
Qed.
Lemma swap_memory_update_snd:
forall ctx smem u1 u2 maxidx sb ops,
valid_smemory maxidx smem ->
valid_smemory_update maxidx u1 ->
valid_smemory_update maxidx u2 ->
valid_bindings maxidx sb ops ->
swap_memory_update ctx u1 u2 maxidx sb = true ->
forall model mem strg exts,
is_model (ctx_cs ctx) model = true ->
exists mem' : memory,
eval_smemory (u1::u2::smem) maxidx sb model mem strg exts ops = Some mem' /\
eval_smemory (u2::u1::smem) maxidx sb model mem strg exts ops = Some mem'.
Proof.
intros ctx smem u1 u2 maxidx sb ops.
intros H_valid_smem H_valid_u1 H_valid_u2 H_valid_sb H_swap_mem_u.
intros model mem strg exts.
intros H_is_model.
pose proof (valid_smemory_when_extended_with_valid_update maxidx u1 smem H_valid_u1 H_valid_smem) as H_valid_u1_smem.
pose proof (valid_smemory_when_extended_with_valid_update maxidx u2 (u1::smem) H_valid_u2 H_valid_u1_smem) as H_valid_u2_u1_smem.
pose proof (valid_smemory_when_extended_with_valid_update maxidx u2 smem H_valid_u2 H_valid_smem) as H_valid_u2_smem.
pose proof (valid_smemory_when_extended_with_valid_update maxidx u1 (u2::smem) H_valid_u1 H_valid_u2_smem) as H_valid_u1_u2_smem.
pose proof (eval_smemory_succ maxidx sb model mem strg exts ops (u1::u2::smem) H_valid_u1_u2_smem H_valid_sb) as H_eval_u1_u2_smem.
pose proof (eval_smemory_succ maxidx sb model mem strg exts ops (u2::u1::smem) H_valid_u2_u1_smem H_valid_sb) as H_eval_u2_u1_smem.
destruct H_eval_u1_u2_smem as [mem1 H_eval_u1_u2_smem].
destruct H_eval_u2_u1_smem as [mem2 H_eval_u2_u1_smem].
unfold eval_smemory in H_eval_u1_u2_smem.
destruct (map_option (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx sb ops)) (u1 :: u2 :: smem)) as [updates1|] eqn:E_mo1; try discriminate.
injection H_eval_u1_u2_smem as H_eval_u1_u2_smem.
unfold eval_smemory in H_eval_u2_u1_smem.
destruct (map_option (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx sb ops)) (u2 :: u1 :: smem)) as [updates2|] eqn:E_mo2; try discriminate.
injection H_eval_u2_u1_smem as H_eval_u2_u1_smem.
pose proof (map_option_split_2 (memory_update sstack_val) (memory_update EVMWord) (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx sb ops)) smem updates1 u1 u2 E_mo1) as E_mo1_split.
destruct E_mo1_split as [u1v1 [u2v1 [updates1' [H_updates1 [H_u1v1 [H_u2v1 H_mo1_0]]]]]].
pose proof (map_option_split_2 (memory_update sstack_val) (memory_update EVMWord) (instantiate_memory_update (fun sv : sstack_val => eval_sstack_val sv model mem strg exts maxidx sb ops)) smem updates2 u2 u1 E_mo2) as E_mo2_split.
destruct E_mo2_split as [u2v2 [u1v2 [updates2' [H_updates2 [H_u2v2 [H_u1v2 H_mo2_0]]]]]].
assert(H_updates1'_eq_updates2': updates1' = updates2'). rewrite H_mo2_0 in H_mo1_0. injection H_mo1_0 as H_mo1_0. rewrite H_mo1_0. reflexivity.
assert(H_u1v1_u1v2: u1v1=u1v2). rewrite H_u1v2 in H_u1v1. injection H_u1v1 as H_u1v1. rewrite H_u1v1. reflexivity.
assert(H_u2v1_u2v2: u2v1=u2v2). rewrite H_u2v2 in H_u2v1. injection H_u2v1 as H_u2v1. rewrite H_u2v1. reflexivity.
rewrite <- H_updates1'_eq_updates2' in H_updates2.
rewrite <- H_u1v1_u1v2 in H_updates2.
rewrite <- H_u2v1_u2v2 in H_updates2.
rewrite H_updates1 in H_eval_u1_u2_smem.
rewrite H_updates2 in H_eval_u2_u1_smem.
unfold update_memory in H_eval_u1_u2_smem.
fold update_memory in H_eval_u1_u2_smem.
unfold update_memory in H_eval_u2_u1_smem.
fold update_memory in H_eval_u2_u1_smem.
destruct u1 as [soffset1 svalue1|soffset1 svalue1] eqn:E_u1;
destruct u2 as [soffset2 svalue2|soffset2 svalue2] eqn:E_u2.
+ unfold instantiate_memory_update in H_u1v1.
destruct (eval_sstack_val soffset1 model mem strg exts maxidx sb ops) as [offset1_v|] eqn:E_eval_soffset1; try discriminate.
destruct (eval_sstack_val svalue1 model mem strg exts maxidx sb ops) as [svalue1_v|] eqn:E_eval_svalue1; try discriminate.
injection H_u1v1 as H_u1v1.
rewrite <- H_u1v1 in H_eval_u1_u2_smem.
rewrite <- H_u1v1 in H_eval_u2_u1_smem.
unfold instantiate_memory_update in H_u2v1.
destruct (eval_sstack_val soffset2 model mem strg exts maxidx sb ops) as [offset2_v|] eqn:E_eval_soffset2; try discriminate.
destruct (eval_sstack_val svalue2 model mem strg exts maxidx sb ops) as [svalue2_v|] eqn:E_eval_svalue2; try discriminate.
injection H_u2v1 as H_u2v1.
rewrite <- H_u2v1 in H_eval_u2_u1_smem.
rewrite <- H_u2v1 in H_eval_u1_u2_smem.
simpl in H_eval_u1_u2_smem.
simpl in H_eval_u2_u1_smem.
unfold mstore in H_eval_u1_u2_smem.
unfold mstore in H_eval_u2_u1_smem.
unfold eval_smemory.
rewrite E_mo1.
rewrite E_mo2.
rewrite H_updates1.
rewrite H_updates2.
rewrite <- H_u1v1.
rewrite <- H_u2v1.
unfold update_memory.
fold update_memory.
unfold update_memory'.
unfold mstore.
simpl in H_valid_u1.
destruct H_valid_u1 as [H_valid_soffset1 H_valid_svalue1].
simpl in H_valid_u2.
destruct H_valid_u2 as [H_valid_soffset2 H_valid_svalue2].
unfold swap_memory_update in H_swap_mem_u.
destruct (follow_in_smap soffset1 maxidx sb) eqn:E_follow_in_smap_soffset1; try discriminate.
destruct f; try discriminate.
destruct smv; try discriminate.
destruct (follow_in_smap soffset2 maxidx sb) eqn:E_follow_in_smap_soffset2; try discriminate.
destruct f; try discriminate.
destruct smv; try discriminate.
destruct val; destruct val0; try discriminate.
* assert(E_eval_soffset1_aux := E_eval_soffset1).
unfold eval_sstack_val in E_eval_soffset1_aux.
unfold eval_sstack_val' in E_eval_soffset1_aux.
fold eval_sstack_val' in E_eval_soffset1_aux.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1_aux.
injection E_eval_soffset1_aux as E_eval_soffset1_aux.
assert(E_eval_soffset2_aux := E_eval_soffset2).
unfold eval_sstack_val in E_eval_soffset2_aux.
unfold eval_sstack_val' in E_eval_soffset2_aux.
fold eval_sstack_val' in E_eval_soffset2_aux.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2_aux.
injection E_eval_soffset2_aux as E_eval_soffset2_aux.
rewrite E_eval_soffset1_aux in H_swap_mem_u.
rewrite E_eval_soffset2_aux in H_swap_mem_u.
assert( H_swap_mem_u_le: (wordToN offset2_v + 32 <=? wordToN offset1_v)%N = true).
pose proof (n_lt_m_implies_n_plus_1_le_m (wordToN offset2_v + 31) (wordToN offset1_v) H_swap_mem_u) as H_swap_mem_u_le_aux.
rewrite <- N.add_assoc in H_swap_mem_u_le_aux.
simpl in H_swap_mem_u_le_aux.
apply H_swap_mem_u_le_aux.
pose proof (mstore_non_overlap_updates BytesInEVMWord BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) svalue2_v (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_lshift_wrt_ctx_snd ctx (InVar var) (Val val) 31 H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_var [H_eval_val H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_val.
simpl in H_eval_val.
rewrite follow_smap_V in H_eval_val.
injection H_eval_val as H_eval_val.
rewrite <- H_eval_var in H_cond.
rewrite <- H_eval_val in H_cond.
rewrite E_eval_soffset1 in H_cond.
rewrite E_eval_soffset2 in H_cond.
rewrite <- N.ltb_lt in H_cond.
assert( H_swap_mem_u_le: (wordToN offset2_v + 32 <=? wordToN offset1_v)%N = true).
pose proof (n_lt_m_implies_n_plus_1_le_m (wordToN offset2_v + 31) (wordToN offset1_v) H_cond) as H_swap_mem_u_le_aux.
rewrite <- N.add_assoc in H_swap_mem_u_le_aux.
simpl in H_swap_mem_u_le_aux.
apply H_swap_mem_u_le_aux.
pose proof (mstore_non_overlap_updates BytesInEVMWord BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) svalue2_v (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_lshift_wrt_ctx_snd ctx (Val val) (InVar var) 31 H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_val [H_eval_var H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_val.
simpl in H_eval_val.
rewrite follow_smap_V in H_eval_val.
injection H_eval_val as H_eval_val.
rewrite <- H_eval_var in H_cond.
rewrite <- H_eval_val in H_cond.
rewrite E_eval_soffset1 in H_cond.
rewrite E_eval_soffset2 in H_cond.
rewrite <- N.ltb_lt in H_cond.
assert( H_swap_mem_u_le: (wordToN offset2_v + 32 <=? wordToN offset1_v)%N = true).
pose proof (n_lt_m_implies_n_plus_1_le_m (wordToN offset2_v + 31) (wordToN offset1_v) H_cond) as H_swap_mem_u_le_aux.
rewrite <- N.add_assoc in H_swap_mem_u_le_aux.
simpl in H_swap_mem_u_le_aux.
apply H_swap_mem_u_le_aux.
pose proof (mstore_non_overlap_updates BytesInEVMWord BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) svalue2_v (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_lshift_wrt_ctx_snd ctx (InVar var0) (InVar var) 31 H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_var0 [H_eval_var H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_var0.
simpl in H_eval_var0.
rewrite follow_smap_InStackVar in H_eval_var0.
injection H_eval_var0 as H_eval_var0.
rewrite <- H_eval_var in H_cond.
rewrite <- H_eval_var0 in H_cond.
rewrite E_eval_soffset1 in H_cond.
rewrite E_eval_soffset2 in H_cond.
rewrite <- N.ltb_lt in H_cond.
assert( H_swap_mem_u_le: (wordToN offset2_v + 32 <=? wordToN offset1_v)%N = true).
pose proof (n_lt_m_implies_n_plus_1_le_m (wordToN offset2_v + 31) (wordToN offset1_v) H_cond) as H_swap_mem_u_le_aux.
rewrite <- N.add_assoc in H_swap_mem_u_le_aux.
simpl in H_swap_mem_u_le_aux.
apply H_swap_mem_u_le_aux.
pose proof (mstore_non_overlap_updates BytesInEVMWord BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) svalue2_v (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite H_eval_u2_u1_smem; reflexivity.
+ unfold instantiate_memory_update in H_u1v1.
destruct (eval_sstack_val soffset1 model mem strg exts maxidx sb ops) as [offset1_v|] eqn:E_eval_soffset1; try discriminate.
destruct (eval_sstack_val svalue1 model mem strg exts maxidx sb ops) as [svalue1_v|] eqn:E_eval_svalue1; try discriminate.
injection H_u1v1 as H_u1v1.
rewrite <- H_u1v1 in H_eval_u1_u2_smem.
rewrite <- H_u1v1 in H_eval_u2_u1_smem.
unfold instantiate_memory_update in H_u2v1.
destruct (eval_sstack_val soffset2 model mem strg exts maxidx sb ops) as [offset2_v|] eqn:E_eval_soffset2; try discriminate.
destruct (eval_sstack_val svalue2 model mem strg exts maxidx sb ops) as [svalue2_v|] eqn:E_eval_svalue2; try discriminate.
injection H_u2v1 as H_u2v1.
rewrite <- H_u2v1 in H_eval_u2_u1_smem.
rewrite <- H_u2v1 in H_eval_u1_u2_smem.
simpl in H_eval_u1_u2_smem.
simpl in H_eval_u2_u1_smem.
unfold mstore in H_eval_u1_u2_smem.
unfold mstore in H_eval_u2_u1_smem.
unfold eval_smemory.
rewrite E_mo1.
rewrite E_mo2.
rewrite H_updates1.
rewrite H_updates2.
rewrite <- H_u1v1.
rewrite <- H_u2v1.
unfold update_memory.
fold update_memory.
unfold update_memory'.
unfold mstore.
unfold swap_memory_update in H_swap_mem_u.
destruct (follow_in_smap soffset1 maxidx sb) eqn:E_follow_in_smap_soffset1; try discriminate.
destruct f; try discriminate.
destruct smv; try discriminate.
destruct (follow_in_smap soffset2 maxidx sb) eqn:E_follow_in_smap_soffset2; try discriminate.
destruct f; try discriminate.
destruct smv; try discriminate.
destruct val; destruct val0; try discriminate.
* assert(E_eval_soffset1_aux := E_eval_soffset1).
unfold eval_sstack_val in E_eval_soffset1_aux.
unfold eval_sstack_val' in E_eval_soffset1_aux.
fold eval_sstack_val' in E_eval_soffset1_aux.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1_aux.
injection E_eval_soffset1_aux as E_eval_soffset1_aux.
assert(E_eval_soffset2_aux := E_eval_soffset2).
unfold eval_sstack_val in E_eval_soffset2_aux.
unfold eval_sstack_val' in E_eval_soffset2_aux.
fold eval_sstack_val' in E_eval_soffset2_aux.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2_aux.
injection E_eval_soffset2_aux as E_eval_soffset2_aux.
rewrite E_eval_soffset1_aux in H_swap_mem_u.
rewrite E_eval_soffset2_aux in H_swap_mem_u.
assert( H_swap_mem_u_le: (wordToN offset2_v + 1 <=? wordToN offset1_v)%N = true).
apply n_lt_m_implies_n_plus_1_le_m. apply H_swap_mem_u.
pose proof (mstore_non_overlap_updates 1 BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) (split1_byte (svalue2_v : word ((S (pred BytesInEVMWord))*8))) (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite <- H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_wrt_ctx_snd ctx (InVar var) (Val val) H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_var [H_eval_val H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_val.
simpl in H_eval_val.
rewrite follow_smap_V in H_eval_val.
injection H_eval_val as H_eval_val.
rewrite <- H_eval_var in H_cond.
rewrite <- H_eval_val in H_cond.
rewrite E_eval_soffset1 in H_cond.
rewrite E_eval_soffset2 in H_cond.
rewrite <- N.ltb_lt in H_cond.
assert( H_swap_mem_u_le: (wordToN offset2_v + 1 <=? wordToN offset1_v)%N = true).
apply n_lt_m_implies_n_plus_1_le_m. apply H_cond.
pose proof (mstore_non_overlap_updates 1 BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) (split1_byte (svalue2_v : word ((S (pred BytesInEVMWord))*8))) (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite <- H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_wrt_ctx_snd ctx (Val val) (InVar var) H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_val [H_eval_var H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_val.
simpl in H_eval_val.
rewrite follow_smap_V in H_eval_val.
injection H_eval_val as H_eval_val.
rewrite <- H_eval_var in H_cond.
rewrite <- H_eval_val in H_cond.
rewrite E_eval_soffset1 in H_cond.
rewrite E_eval_soffset2 in H_cond.
rewrite <- N.ltb_lt in H_cond.
assert( H_swap_mem_u_le: (wordToN offset2_v + 1 <=? wordToN offset1_v)%N = true).
apply n_lt_m_implies_n_plus_1_le_m. apply H_cond.
pose proof (mstore_non_overlap_updates 1 BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) (split1_byte (svalue2_v : word ((S (pred BytesInEVMWord))*8))) (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite <- H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_wrt_ctx_snd ctx (InVar var0) (InVar var) H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_var0 [H_eval_var H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_var0.
simpl in H_eval_var0.
rewrite follow_smap_InStackVar in H_eval_var0.
injection H_eval_var0 as H_eval_var0.
rewrite <- H_eval_var in H_cond.
rewrite <- H_eval_var0 in H_cond.
rewrite E_eval_soffset1 in H_cond.
rewrite E_eval_soffset2 in H_cond.
rewrite <- N.ltb_lt in H_cond.
assert( H_swap_mem_u_le: (wordToN offset2_v + 1 <=? wordToN offset1_v)%N = true).
apply n_lt_m_implies_n_plus_1_le_m. apply H_cond.
pose proof (mstore_non_overlap_updates 1 BytesInEVMWord (update_memory mem updates1') (wordToN offset2_v) (split1_byte (svalue2_v : word ((S (pred BytesInEVMWord))*8))) (wordToN offset1_v) svalue1_v H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite <- H_eval_u2_u1_smem; reflexivity.
+ unfold instantiate_memory_update in H_u1v1.
destruct (eval_sstack_val soffset1 model mem strg exts maxidx sb ops) as [offset1_v|] eqn:E_eval_soffset1; try discriminate.
destruct (eval_sstack_val svalue1 model mem strg exts maxidx sb ops) as [svalue1_v|] eqn:E_eval_svalue1; try discriminate.
injection H_u1v1 as H_u1v1.
rewrite <- H_u1v1 in H_eval_u1_u2_smem.
rewrite <- H_u1v1 in H_eval_u2_u1_smem.
unfold instantiate_memory_update in H_u2v1.
destruct (eval_sstack_val soffset2 model mem strg exts maxidx sb ops) as [offset2_v|] eqn:E_eval_soffset2; try discriminate.
destruct (eval_sstack_val svalue2 model mem strg exts maxidx sb ops) as [svalue2_v|] eqn:E_eval_svalue2; try discriminate.
injection H_u2v1 as H_u2v1.
rewrite <- H_u2v1 in H_eval_u2_u1_smem.
rewrite <- H_u2v1 in H_eval_u1_u2_smem.
simpl in H_eval_u1_u2_smem.
simpl in H_eval_u2_u1_smem.
unfold mstore in H_eval_u1_u2_smem.
unfold mstore in H_eval_u2_u1_smem.
unfold eval_smemory.
rewrite E_mo1.
rewrite E_mo2.
rewrite H_updates1.
rewrite H_updates2.
rewrite <- H_u1v1.
rewrite <- H_u2v1.
unfold update_memory.
fold update_memory.
unfold update_memory'.
unfold mstore.
unfold swap_memory_update in H_swap_mem_u.
destruct (follow_in_smap soffset1 maxidx sb) eqn:E_follow_in_smap_soffset1; try discriminate.
destruct f; try discriminate.
destruct smv; try discriminate.
destruct (follow_in_smap soffset2 maxidx sb) eqn:E_follow_in_smap_soffset2; try discriminate.
destruct f; try discriminate.
destruct smv; try discriminate.
destruct val; destruct val0; try discriminate.
* assert(E_eval_soffset1_aux := E_eval_soffset1).
unfold eval_sstack_val in E_eval_soffset1_aux.
unfold eval_sstack_val' in E_eval_soffset1_aux.
fold eval_sstack_val' in E_eval_soffset1_aux.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1_aux.
injection E_eval_soffset1_aux as E_eval_soffset1_aux.
assert(E_eval_soffset2_aux := E_eval_soffset2).
unfold eval_sstack_val in E_eval_soffset2_aux.
unfold eval_sstack_val' in E_eval_soffset2_aux.
fold eval_sstack_val' in E_eval_soffset2_aux.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2_aux.
injection E_eval_soffset2_aux as E_eval_soffset2_aux.
rewrite E_eval_soffset1_aux in H_swap_mem_u.
rewrite E_eval_soffset2_aux in H_swap_mem_u.
assert( H_swap_mem_u_le: (wordToN offset2_v + 32 <=? wordToN offset1_v)%N = true).
pose proof (n_lt_m_implies_n_plus_1_le_m (wordToN offset2_v + 31) (wordToN offset1_v) H_swap_mem_u) as H_swap_mem_u_le_aux.
rewrite <- N.add_assoc in H_swap_mem_u_le_aux.
simpl in H_swap_mem_u_le_aux.
apply H_swap_mem_u_le_aux.
pose proof (mstore_non_overlap_updates BytesInEVMWord 1 (update_memory mem updates1') (wordToN offset2_v) svalue2_v (wordToN offset1_v) (split1_byte (svalue1_v : word ((S (pred BytesInEVMWord))*8))) H_swap_mem_u_le) as H_mstore_non_overlap_updates.
rewrite H_mstore_non_overlap_updates.
exists mem2.
split; rewrite <- H_eval_u2_u1_smem; reflexivity.
* pose proof (chk_lt_lshift_wrt_ctx_snd ctx (InVar var) (Val val) 31 H_swap_mem_u model mem strg exts maxidx sb ops H_is_model) as H_chk_lt_lshift_wrt_ctx_snd.
destruct H_chk_lt_lshift_wrt_ctx_snd as [v1 [v2 [ H_eval_var [H_eval_val H_cond]]]].
unfold eval_sstack_val in E_eval_soffset1.
unfold eval_sstack_val' in E_eval_soffset1.
fold eval_sstack_val' in E_eval_soffset1.
rewrite E_follow_in_smap_soffset1 in E_eval_soffset1.
injection E_eval_soffset1 as E_eval_soffset1.
unfold eval_sstack_val in E_eval_soffset2.
unfold eval_sstack_val' in E_eval_soffset2.
fold eval_sstack_val' in E_eval_soffset2.
rewrite E_follow_in_smap_soffset2 in E_eval_soffset2.
injection E_eval_soffset2 as E_eval_soffset2.
unfold eval_sstack_val in H_eval_var.
simpl in H_eval_var.
rewrite follow_smap_InStackVar in H_eval_var.
injection H_eval_var as H_eval_var.
unfold eval_sstack_val in H_eval_val.
simpl in H_eval_val.