replacing omega with lia in some file

1 files changed, 22 insertions, 21 deletions

diff --git a/scheduling/RTLpath.v b/scheduling/RTLpath.v
index 5b34dc16..0f303597 100644
--- a/scheduling/RTLpath.v
+++ b/scheduling/RTLpath.v
@@ -26,6 +26,7 @@ Require Import Coqlib Maps.
 Require Import AST Integers Values Events Memory Globalenvs Smallstep.
 Require Import Op Registers.
 Require Import RTL Linking.
+Require Import Lia.
 
 Declare Scope option_monad_scope.
 
@@ -584,8 +585,8 @@ Lemma wellformed_suffix_path c pm path path':
    exists pc', nth_default_succ c (path-path') pc = Some pc' /\ wellformed_path c pm path' pc'.
 Proof.
   induction 1 as [|m].
-  + intros. enough (path'-path'=0)%nat as ->; [simpl;eauto|omega].
-  + intros pc WF; enough (S m-path'=S (m-path'))%nat as ->; [simpl;eauto|omega].
+  + intros. enough (path'-path'=0)%nat as ->; [simpl;eauto|lia].
+  + intros pc WF; enough (S m-path'=S (m-path'))%nat as ->; [simpl;eauto|lia].
     inversion WF; subst; clear WF; intros; simplify_someHyps.
     intros; simplify_someHyps; eauto.
 Qed.
@@ -602,9 +603,9 @@ Proof.
   intros; exploit fn_path_wf; eauto.
   intro WF.
   set (ps:=path.(psize)).
-  exploit (wellformed_suffix_path (fn_code f) (fn_path f) ps O); omega || eauto.
+  exploit (wellformed_suffix_path (fn_code f) (fn_path f) ps O); lia || eauto.
   destruct 1 as (pc' & NTH_SUCC & WF'); auto.
-  assert (ps - 0 = ps)%nat as HH by omega. rewrite HH in NTH_SUCC. clear HH.
+  assert (ps - 0 = ps)%nat as HH by lia. rewrite HH in NTH_SUCC. clear HH.
   unfold nth_default_succ_inst.
   inversion WF'; clear WF'; subst. simplify_someHyps; eauto.
 Qed.
@@ -619,11 +620,11 @@ Lemma internal_node_path path f path0 pc:
 Proof.
   intros; exploit fn_path_wf; eauto.
   set (ps:=path0.(psize)).
-  intro WF; exploit (wellformed_suffix_path (fn_code f) (fn_path f) ps (ps-path)); eauto. { omega. }
+  intro WF; exploit (wellformed_suffix_path (fn_code f) (fn_path f) ps (ps-path)); eauto. { lia. }
   destruct 1 as (pc' & NTH_SUCC & WF').
-  assert (ps - (ps - path) = path)%nat as HH by omega. rewrite HH in NTH_SUCC. clear HH.
+  assert (ps - (ps - path) = path)%nat as HH by lia. rewrite HH in NTH_SUCC. clear HH.
   unfold nth_default_succ_inst. 
-  inversion WF'; clear WF'; subst. { omega. }
+  inversion WF'; clear WF'; subst. { lia. }
   simplify_someHyps; eauto.
 Qed.
 
@@ -708,7 +709,7 @@ Proof.
       rewrite CONT. auto.
     + intros; try_simplify_someHyps; try congruence.
       eexists. exists i. exists O; simpl. intuition eauto.
-      omega.
+      lia.
 Qed.
 
 Lemma isteps_resize ge path0 path1 f sp rs m pc st: 
@@ -839,15 +840,15 @@ Lemma stuttering path idx stack f sp rs m pc st t s1':
    RTL.step ge (State stack f sp st.(ipc) st.(irs) st.(imem)) t s1' ->
    t = E0 /\ match_inst_states idx s1' (State stack f sp pc rs m).
 Proof.
-  intros PSTEP PATH BOUND CONT RSTEP; exploit (internal_node_path (path.(psize)-(S idx))); omega || eauto.
+  intros PSTEP PATH BOUND CONT RSTEP; exploit (internal_node_path (path.(psize)-(S idx))); lia || eauto.
   intros (i & pc' & Hi & Hpc & DUM).
   unfold nth_default_succ_inst in Hi.
   erewrite isteps_normal_exit in Hi; eauto.
   exploit istep_complete; congruence || eauto.
   intros (SILENT & st0 & STEP0 & EQ).
   intuition; subst; unfold match_inst_states; simpl.
-  intros; refine (State_match _ _ path stack f sp pc rs m _ PATH _ _ _); simpl; omega || eauto.
-  set (ps:=path.(psize)). enough (ps - idx = S (ps - (S idx)))%nat as ->; try omega.
+  intros; refine (State_match _ _ path stack f sp pc rs m _ PATH _ _ _); simpl; lia || eauto.
+  set (ps:=path.(psize)). enough (ps - idx = S (ps - (S idx)))%nat as ->; try lia.
   erewrite <- isteps_step_right; eauto.
 Qed.
 
@@ -876,7 +877,7 @@ Proof.
     destruct (initialize_path (*fn_code f*) (fn_path f) (ipc st0)) as (path0 & Hpath0); eauto.
     exists (path0.(psize)); intuition eauto.
     econstructor; eauto.
-    * enough (path0.(psize)-path0.(psize)=0)%nat as ->; simpl; eauto || omega.
+    * enough (path0.(psize)-path0.(psize)=0)%nat as ->; simpl; eauto || lia.
     * simpl; eauto.
   + generalize Hi; inversion RSTEP; clear RSTEP; subst; (repeat (simplify_someHyp; simpl in * |- * )); try congruence; eauto.
     - (* Icall *)
@@ -899,7 +900,7 @@ Proof.
       destruct (initialize_path (*fn_code f*) (fn_path f) pc') as (path0 & Hpath0); eauto.
       exists path0.(psize); intuition eauto.
       econstructor; eauto.
-      * enough (path0.(psize)-path0.(psize)=0)%nat as ->; simpl; eauto || omega.
+      * enough (path0.(psize)-path0.(psize)=0)%nat as ->; simpl; eauto || lia.
       * simpl; eauto.
    - (* Ijumptable *)
       intros; exploit exec_Ijumptable; eauto.
@@ -908,7 +909,7 @@ Proof.
       destruct (initialize_path (*fn_code f*) (fn_path f) pc') as (path0 & Hpath0); eauto.
       exists path0.(psize); intuition eauto.
       econstructor; eauto.
-      * enough (path0.(psize)-path0.(psize)=0)%nat as ->; simpl; eauto || omega.
+      * enough (path0.(psize)-path0.(psize)=0)%nat as ->; simpl; eauto || lia.
       * simpl; eauto.
   - (* Ireturn *)
       intros; exploit exec_Ireturn; eauto.
@@ -935,7 +936,7 @@ Proof.
   intros PSTEP PATH BOUND RSTEP WF; destruct (st.(icontinue)) eqn: CONT.
   destruct idx as [ | idx].
   + (* path_step on normal_exit *)
-     assert (path.(psize)-0=path.(psize))%nat as HH by omega. rewrite HH in PSTEP. clear HH.
+     assert (path.(psize)-0=path.(psize))%nat as HH by lia. rewrite HH in PSTEP. clear HH.
      exploit normal_exit; eauto.
      intros (s2' & LSTEP & (idx' & MATCH)).
      exists idx'; exists s2'; intuition eauto.
@@ -944,7 +945,7 @@ Proof.
     unfold match_states; exists idx; exists (State stack f sp pc rs m); 
     intuition.
   + (* one or two path_step on early_exit *)
-    exploit (isteps_resize ge (path.(psize) - idx)%nat path.(psize)); eauto; try omega.
+    exploit (isteps_resize ge (path.(psize) - idx)%nat path.(psize)); eauto; try lia.
     clear PSTEP; intros PSTEP.
     (* TODO for clarification: move the assert below into a separate lemma *)
     assert (HPATH0: exists path0, (fn_path f)!(ipc st) = Some path0).
@@ -954,7 +955,7 @@ Proof.
       exploit istep_early_exit; eauto.
       intros (X1 & X2 & EARLY_EXIT).
       destruct st as [cont pc0 rs0 m0]; simpl in * |- *; intuition subst.
-      exploit (internal_node_path path0); omega || eauto.
+      exploit (internal_node_path path0); lia || eauto.
       intros (i' & pc' & Hi' & Hpc' & ENTRY).
       unfold nth_default_succ_inst in Hi'.
       erewrite isteps_normal_exit in Hi'; eauto.
@@ -976,8 +977,8 @@ Proof.
       - simpl; eauto.
     * (* single step case *)
       exploit (stuttering path1 ps stack f sp (irs st) (imem st) (ipc st)); simpl; auto.
-      - { rewrite Hpath1size; enough (S ps-S ps=0)%nat as ->; try omega.  simpl; eauto. }
-      - omega.
+      - { rewrite Hpath1size; enough (S ps-S ps=0)%nat as ->; try lia.  simpl; eauto. }
+      - lia.
       - simpl; eauto.
       - simpl; eauto.
       - intuition subst.
@@ -1002,7 +1003,7 @@ Proof.
       exists path.(psize). constructor; auto.
       econstructor; eauto.
       - set (ps:=path.(psize)). enough (ps-ps=O)%nat as ->; simpl; eauto.
-        omega.
+        lia.
       - simpl; auto.
   + (* exec_function_external *)
     destruct f; simpl in H3 |-; inversion H3; subst; clear H3.
@@ -1021,7 +1022,7 @@ Proof.
       exists path.(psize). constructor; auto.
       econstructor; eauto.
       - set (ps:=path.(psize)). enough (ps-ps=O)%nat as ->; simpl; eauto.
-        omega.
+        lia.
       - simpl; auto.
 Qed.