hoare logic: rules for assert

examples/hoare_logic/wp/wp_WP_WP_WP_parameter_wp_1.v

+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import ZArith.
+Require Import Rbase.
+Definition unit  := unit.
+
+Parameter qtmark : Type.
+
+Parameter at1: forall (a:Type), a -> qtmark -> a.
+
+Implicit Arguments at1.
+
+Parameter old: forall (a:Type), a -> a.
+
+Implicit Arguments old.
+
+Definition implb(x:bool) (y:bool): bool := match (x,
+  y) with
+  | (true, false) => false
+  | (_, _) => true
+  end.
+
+Inductive datatype  :=
+  | Tint : datatype 
+  | Tbool : datatype .
+
+Inductive operator  :=
+  | Oplus : operator 
+  | Ominus : operator 
+  | Omult : operator 
+  | Ole : operator .
+
+Definition ident  := Z.
+
+Inductive term  :=
+  | Tconst : Z -> term 
+  | Tvar : Z -> term 
+  | Tderef : Z -> term 
+  | Tbin : term -> operator -> term -> term .
+
+Inductive fmla  :=
+  | Fterm : term -> fmla 
+  | Fand : fmla -> fmla -> fmla 
+  | Fnot : fmla -> fmla 
+  | Fimplies : fmla -> fmla -> fmla 
+  | Fforall : Z -> datatype -> fmla -> fmla .
+
+Inductive value  :=
+  | Vint : Z -> value 
+  | Vbool : bool -> value .
+
+Parameter map : forall (a:Type) (b:Type), Type.
+
+Parameter get: forall (a:Type) (b:Type), (map a b) -> a -> b.
+
+Implicit Arguments get.
+
+Parameter set: forall (a:Type) (b:Type), (map a b) -> a -> b -> (map a b).
+
+Implicit Arguments set.
+
+Axiom Select_eq : forall (a:Type) (b:Type), forall (m:(map a b)),
+  forall (a1:a) (a2:a), forall (b1:b), (a1 = a2) -> ((get (set m a1 b1)
+  a2) = b1).
+
+Axiom Select_neq : forall (a:Type) (b:Type), forall (m:(map a b)),
+  forall (a1:a) (a2:a), forall (b1:b), (~ (a1 = a2)) -> ((get (set m a1 b1)
+  a2) = (get m a2)).
+
+Parameter const: forall (b:Type) (a:Type), b -> (map a b).
+
+Set Contextual Implicit.
+Implicit Arguments const.
+Unset Contextual Implicit.
+
+Axiom Const : forall (b:Type) (a:Type), forall (b1:b) (a1:a), ((get (const(
+  b1):(map a b)) a1) = b1).
+
+Definition var_env  := (map Z value).
+
+Definition ref_env  := (map Z value).
+
+Inductive state  :=
+  | mk_state : (map Z value) -> (map Z value) -> state .
+
+Definition ref_env1(u:state): (map Z value) :=
+  match u with
+  | (mk_state _ ref_env2) => ref_env2
+  end.
+
+Definition var_env1(u:state): (map Z value) :=
+  match u with
+  | (mk_state var_env2 _) => var_env2
+  end.
+
+Definition eval_bin(x:value) (op:operator) (y:value) (res:value): Prop :=
+  match (x,
+  y) with
+  | ((Vint x1), (Vint y1)) =>
+      match op with
+      | Oplus => (res = (Vint (x1 + y1)%Z))
+      | Ominus => (res = (Vint (x1 - y1)%Z))
+      | Omult => (res = (Vint (x1 * y1)%Z))
+      | Ole => ((x1 <= y1)%Z -> (res = (Vbool true))) /\ ((~ (x1 <= y1)%Z) ->
+          (res = (Vbool false)))
+      end
+  | (_, _) => False
+  end.
+
+Definition get_refenv(i:Z) (e:(map Z value)) (r:value): Prop := ((get e
+  i) = r).
+
+Inductive eval_term : state -> term -> value -> Prop :=
+  | eval_const : forall (s:state) (n:Z), (eval_term s (Tconst n) (Vint n))
+  | eval_var : forall (s:state) (i:Z) (res:value), (get_refenv i (var_env1 s)
+      res) -> (eval_term s (Tvar i) res)
+  | eval_deref : forall (s:state) (i:Z) (res:value), (get_refenv i
+      (ref_env1 s) res) -> (eval_term s (Tderef i) res)
+  | eval_bin1 : forall (s:state) (op:operator) (t1:term) (t2:term) (r1:value)
+      (r2:value) (r:value), (eval_term s t1 r1) -> ((eval_term s t2 r2) ->
+      ((eval_bin r1 op r2 r) -> (eval_term s (Tbin t1 op t2) r))).
+
+Inductive eval_fmla : state -> fmla -> bool -> Prop :=
+  | eval_term1 : forall (s:state) (t:term) (b:bool), (eval_term s t
+      (Vbool b)) -> (eval_fmla s (Fterm t) b)
+  | eval_and : forall (s:state) (f1:fmla) (f2:fmla) (b1:bool) (b2:bool),
+      (eval_fmla s f1 b1) -> ((eval_fmla s f2 b2) -> (eval_fmla s (Fand f1
+      f2) (andb b1 b2)))
+  | eval_not : forall (s:state) (f:fmla) (b:bool), (eval_fmla s f b) ->
+      (eval_fmla s (Fnot f) (negb b))
+  | eval_impl : forall (s:state) (f1:fmla) (f2:fmla) (b1:bool) (b2:bool),
+      (eval_fmla s f1 b1) -> ((eval_fmla s f2 b2) -> (eval_fmla s
+      (Fimplies f1 f2) (implb b1 b2)))
+  | eval_forall_int_true : forall (s:state) (x:Z) (f:fmla), (forall (n:Z),
+      (eval_fmla (mk_state (set (var_env1 s) x (Vint n)) (ref_env1 s)) f
+      true)) -> (eval_fmla s (Fforall x Tint f) true).
+
+Parameter subst_term: term -> Z -> term -> term.
+
+
+Axiom subst_term_def : forall (e:term) (x:Z) (t:term),
+  match e with
+  | (Tconst _) => ((subst_term e x t) = e)
+  | (Tvar _) => ((subst_term e x t) = e)
+  | (Tderef y) => ((x = y) -> ((subst_term e x t) = t)) /\ ((~ (x = y)) ->
+      ((subst_term e x t) = e))
+  | (Tbin e1 op e2) => ((subst_term e x t) = (Tbin (subst_term e1 x t) op
+      (subst_term e2 x t)))
+  end.
+
+Axiom eval_subst_term : forall (s:state) (e:term) (x:Z) (t:term) (r:value)
+  (v:value), (eval_term s t r) -> ((eval_term s (subst_term e x t) v) <->
+  (eval_term (mk_state (var_env1 s) (set (ref_env1 s) x r)) e v)).
+
+Set Implicit Arguments.
+Fixpoint subst(f:fmla) (x:Z) (t:term) {struct f}: fmla :=
+  match f with
+  | (Fterm e) => (Fterm (subst_term e x t))
+  | (Fand f1 f2) => (Fand (subst f1 x t) (subst f2 x t))
+  | (Fnot f1) => (Fnot (subst f1 x t))
+  | (Fimplies f1 f2) => (Fimplies (subst f1 x t) (subst f2 x t))
+  | (Fforall y ty f1) => (Fforall y ty (subst f1 x t))
+  end.
+Unset Implicit Arguments.
+
+Axiom eval_subst : forall (s:state) (f:fmla) (x:Z) (t:term) (r:value)
+  (b:bool), (eval_fmla s (subst f x t) b) <->
+  (eval_fmla (mk_state (var_env1 s) (set (ref_env1 s) x r)) f b).
+
+Inductive stmt  :=
+  | Sskip : stmt 
+  | Sassign : Z -> term -> stmt 
+  | Sseq : stmt -> stmt -> stmt 
+  | Sif : term -> stmt -> stmt -> stmt 
+  | Swhile : term -> fmla -> stmt -> stmt .
+
+Axiom check_skip : forall (s:stmt), (s = Sskip) \/ ~ (s = Sskip).
+
+Inductive one_step : state -> stmt -> state -> stmt -> Prop :=
+  | one_step_assign : forall (s:state) (x:Z) (e:term) (r:value), (eval_term s
+      e r) -> (one_step s (Sassign x e) (mk_state (var_env1 s)
+      (set (ref_env1 s) x r)) Sskip)
+  | one_step_seq : forall (s:state) (sqt:state) (i1:stmt) (i1qt:stmt)
+      (i2:stmt), (one_step s i1 sqt i1qt) -> (one_step s (Sseq i1 i2) sqt
+      (Sseq i1qt i2))
+  | one_step_seq_skip : forall (s:state) (i:stmt), (one_step s (Sseq Sskip i)
+      s i)
+  | one_step_if_true : forall (s:state) (e:term) (i1:stmt) (i2:stmt),
+      (eval_term s e (Vbool true)) -> (one_step s (Sif e i1 i2) s i1)
+  | one_step_if_false : forall (s:state) (e:term) (i1:stmt) (i2:stmt),
+      (eval_term s e (Vbool false)) -> (one_step s (Sif e i1 i2) s i2)
+  | one_step_while_true : forall (s:state) (e:term) (inv:fmla) (i:stmt),
+      (eval_fmla s inv true) -> ((eval_term s e (Vbool true)) -> (one_step s
+      (Swhile e inv i) s (Sseq i (Swhile e inv i))))
+  | one_step_while_false : forall (s:state) (e:term) (inv:fmla) (i:stmt),
+      (eval_fmla s inv true) -> ((eval_term s e (Vbool false)) -> (one_step s
+      (Swhile e inv i) s Sskip)).
+
+Inductive many_steps : state -> stmt -> state -> stmt -> Z -> Prop :=
+  | many_steps_refl : forall (s:state) (i:stmt), (many_steps s i s i 0%Z)
+  | many_steps_trans : forall (s1:state) (s2:state) (s3:state) (i1:stmt)
+      (i2:stmt) (i3:stmt) (n:Z), (one_step s1 i1 s2 i2) -> ((many_steps s2 i2
+      s3 i3 n) -> (many_steps s1 i1 s3 i3 (n + 1%Z)%Z)).
+
+Axiom steps_non_neg : forall (s1:state) (s2:state) (i1:stmt) (i2:stmt) (n:Z),
+  (many_steps s1 i1 s2 i2 n) -> (0%Z <= n)%Z.
+
+Axiom many_steps_seq : forall (s1:state) (s3:state) (i1:stmt) (i2:stmt)
+  (n:Z), (many_steps s1 (Sseq i1 i2) s3 Sskip n) -> exists s2:state,
+  exists n1:Z, exists n2:Z, (many_steps s1 i1 s2 Sskip n1) /\ ((many_steps s2
+  i2 s3 Sskip n2) /\ (n = ((1%Z + n1)%Z + n2)%Z)).
+
+Definition valid_fmla(p:fmla): Prop := forall (s:state), (eval_fmla s p
+  true).
+
+Definition valid_triple(p:fmla) (i:stmt) (q:fmla): Prop := forall (s:state),
+  (eval_fmla s p true) -> forall (sqt:state) (n:Z), (many_steps s i sqt Sskip
+  n) -> (eval_fmla sqt q true).
+
+Axiom skip_rule : forall (q:fmla), (valid_triple q Sskip q).
+
+Axiom assign_rule : forall (q:fmla) (x:Z) (e:term), (valid_triple (subst q x
+  e) (Sassign x e) q).
+
+Axiom seq_rule : forall (p:fmla) (q:fmla) (r:fmla) (i1:stmt) (i2:stmt),
+  ((valid_triple p i1 r) /\ (valid_triple r i2 q)) -> (valid_triple p
+  (Sseq i1 i2) q).
+
+Axiom if_rule : forall (e:term) (p:fmla) (q:fmla) (i1:stmt) (i2:stmt),
+  ((valid_triple (Fand p (Fterm e)) i1 q) /\ (valid_triple (Fand p
+  (Fnot (Fterm e))) i2 q)) -> (valid_triple p (Sif e i1 i2) q).
+
+Axiom while_rule : forall (e:term) (inv:fmla) (i:stmt),
+  (valid_triple (Fand (Fterm e) inv) i inv) -> (valid_triple inv (Swhile e
+  inv i) (Fand (Fnot (Fterm e)) inv)).
+
+Axiom consequence_rule : forall (p:fmla) (pqt:fmla) (q:fmla) (qqt:fmla)
+  (i:stmt), (valid_fmla (Fimplies pqt p)) -> ((valid_triple p i q) ->
+  ((valid_fmla (Fimplies q qqt)) -> (valid_triple pqt i qqt))).
+
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+(* DO NOT EDIT BELOW *)
+
+Theorem WP_parameter_wp : forall (i:stmt), forall (q:fmla),
+  match i with
+  | Sskip => True
+  | (Sseq i1 i2) => True
+  | (Sassign x e) => True
+  | (Sif e i1 i2) => forall (result:fmla), (valid_triple result i1 q) ->
+      forall (result1:fmla), (valid_triple result1 i2 q) ->
+      (valid_triple (Fand (Fimplies (Fterm e) result)
+      (Fimplies (Fnot (Fterm e)) result1)) i q)
+  | (Swhile e inv i1) => True
+  end.
+(* YOU MAY EDIT THE PROOF BELOW *)
+destruct i; auto.
+intros q r1 H1 r2 H2. 
+apply if_rule.
+split.
+apply consequence_rule with (2:= H1).
+Focus 2.
+red.
+intro.
+
+apply eval_impl.
+simpl.
+Qed.
+(* DO NOT EDIT BELOW *)
+
+

examples/hoare_logic/wp_total.mlw

@@ -299,6 +299,10 @@ lemma assert_rule:
   forall f p:fmla. valid_fmla (Fimplies p f) ->
   valid_triple p (Sassert f) p
 
+lemma assert_rule_ext:
+  forall f p:fmla.
+  valid_triple (Fimplies f p) (Sassert f) p
+
 lemma while_rule:
   forall e:term, inv:fmla, i:stmt.
   valid_triple (Fand (Fterm e) inv) i inv ->
@@ -335,15 +339,15 @@ module WP
     | Sseq i1 i2 -> wp i1 (wp i2 q)
     | Sassign x e ->
        (*
-         let id = fresh ? in Flet id e (subst q x (Tvar id))
+         let id = fresh (vars q) in Flet id e (subst q x (Tvar id))
        *)
        subst q x e
     | Sif e i1 i2 ->
         Fand (Fimplies (Fterm e) (wp i1 q))
              (Fimplies (Fnot (Fterm e)) (wp i2 q))
     | Sassert f ->
-       (* Fimplies f q (* liberal wp, no termination requires *)*)
-       Fand f q
+       Fimplies f q (* liberal wp, no termination requires *)
+       (* Fand f q *) (* strict wp, termination required *)
     | Swhile e inv i ->
         Fand inv
           ((*Fforall*) (Fand

examples/hoare_logic/wp_total/why3session.xml

@@ -292,9 +292,23 @@
      <result status="valid" time="0.49"/>
     </proof>
    </goal>
+   <goal
+    name="assert_rule_ext"
+    sum="6ef422accb858e96de2d1c57b650517d"
+    proved="true"
+    expanded="false"
+    shape="avalid_tripleaFimpliesV0V1aSassertV0V1F">
+    <proof
+     prover="coq"
+     timelimit="5"
+     edited="wp_total_Imp_assert_rule_ext_1.v"
+     obsolete="false">
+     <result status="valid" time="0.64"/>
+    </proof>
+   </goal>
    <goal
     name="while_rule"
-    sum="bec5834960c3c86b3f9f99cc18738d22"
+    sum="9415c44e0de53e2b8ab66c98e1aad735"
     proved="true"
     expanded="false"
     shape="avalid_tripleV1aSwhileV0V1V2aFandaFnotaFtermV0V1Iavalid_tripleaFandaFtermV0V1V2V1F">
@@ -303,12 +317,12 @@
      timelimit="5"
      edited="wp_total_Imp_while_rule_1.v"
      obsolete="false">
-     <result status="valid" time="0.89"/>
+     <result status="valid" time="0.75"/>
     </proof>
    </goal>
    <goal
     name="while_rule_ext"
-    sum="8794717fd4ea98f868bff9bef70ba2e9"
+    sum="b0e30a2a5ef7cc94e42779e850a6e322"
     proved="true"
     expanded="false"
     shape="avalid_tripleV2aSwhileV0V1V3aFandaFnotaFtermV0V2Iavalid_tripleaFandaFtermV0V2V3V2Iavalid_fmlaaFimpliesV2V1F">
@@ -317,12 +331,12 @@
      timelimit="5"
      edited="wp_total_Imp_while_rule_ext_1.v"
      obsolete="false">
-     <result status="valid" time="0.68"/>
+     <result status="valid" time="0.92"/>
     </proof>
    </goal>
    <goal
     name="consequence_rule"
-    sum="6d2f7c295257b282b3949c9e1578b827"
+    sum="22eda61fc378d4aff202e97861225890"
     proved="true"
     expanded="false"
     shape="avalid_tripleV1V4V3Iavalid_fmlaaFimpliesV2V3Iavalid_tripleV0V4V2Iavalid_fmlaaFimpliesV1V0F">
@@ -331,14 +345,14 @@
      timelimit="5"
      edited=""
      obsolete="false">
-     <result status="valid" time="0.99"/>
+     <result status="valid" time="1.13"/>
     </proof>
     <proof
      prover="z3"
      timelimit="5"
      edited=""
      obsolete="false">
-     <result status="valid" time="0.07"/>
+     <result status="valid" time="0.08"/>
     </proof>
    </goal>
   </theory>
@@ -349,15 +363,15 @@
    <goal
     name="WP_parameter wp"
     expl="parameter wp"
-    sum="f45f813e5159661bb5111be4d54b8790"
+    sum="fcf6c0443719c76bb3dd7ad8e2f3d53e"
     proved="false"
     expanded="true"
-    shape="CV0aSskipavalid_tripleV1V0V1aSseqVVavalid_tripleV5V0V1Iavalid_tripleV5V2V4FIavalid_tripleV4V3V1FaSassignVVavalid_tripleasubstV1V6V7V0V1aSifVVVavalid_tripleaFandaFimpliesaFtermV8V11aFimpliesaFnotaFtermV8V12V0V1Iavalid_tripleV12V10V1FIavalid_tripleV11V9V1FaSassertVavalid_tripleaFandV13V1V0V1aSwhileVVVavalid_tripleaFandV15aFandaFimpliesaFandaFtermV14V15V17aFimpliesaFandaFnotaFtermV14V15V1V0V1Iavalid_tripleV17V16V15FFF">
+    shape="CV0aSskipavalid_tripleV1V0V1aSseqVVavalid_tripleV5V0V1Iavalid_tripleV5V2V4FIavalid_tripleV4V3V1FaSassignVVavalid_tripleasubstV1V6V7V0V1aSifVVVavalid_tripleaFandaFimpliesaFtermV8V11aFimpliesaFnotaFtermV8V12V0V1Iavalid_tripleV12V10V1FIavalid_tripleV11V9V1FaSassertVavalid_tripleaFimpliesV13V1V0V1aSwhileVVVavalid_tripleaFandV15aFandaFimpliesaFandaFtermV14V15V17aFimpliesaFandaFnotaFtermV14V15V1V0V1Iavalid_tripleV17V16V15FFF">
     <proof
      prover="coq"
      timelimit="5"
      edited="wp_total_WP_WP_WP_parameter_wp_2.v"
-     obsolete="false">
+     obsolete="true">
      <result status="unknown" time="0.66"/>
     </proof>
     <transf
@@ -367,7 +381,7 @@
      <goal
       name="WP_parameter wp.1"
       expl="parameter wp"
-      sum="681cb4de3c5050ec5b11c56595edba80"
+      sum="e39ef2792789f35bc7b90f25ed79b298"
       proved="true"
       expanded="false"
       shape="CV0aSskipavalid_tripleV1V0V1aSseqVVtaSassignVVtaSifVVVtaSassertVtaSwhileVVVtFF">
@@ -376,13 +390,13 @@
        timelimit="5"
        edited=""
        obsolete="false">
-       <result status="valid" time="0.06"/>
+       <result status="valid" time="0.05"/>
       </proof>
      </goal>
      <goal
       name="WP_parameter wp.2"
       expl="parameter wp"
-      sum="9323fd1e9b4f9bd9e199ad0082179385"
+      sum="35730568229c8ac688137a37e2315371"
       proved="true"
       expanded="false"
       shape="CV0aSskiptaSseqVVavalid_tripleV5V0V1Iavalid_tripleV5V2V4FIavalid_tripleV4V3V1FaSassignVVtaSifVVVtaSassertVtaSwhileVVVtFF">
@@ -391,13 +405,13 @@
        timelimit="5"
        edited=""
        obsolete="false">
-       <result status="valid" time="0.06"/>
+       <result status="valid" time="0.05"/>
       </proof>
      </goal>
      <goal
       name="WP_parameter wp.3"
       expl="parameter wp"
-      sum="78deb10676cae77d7398c31af63dcad8"
+      sum="f2d2133eb159207f51a4abc3674e7ac4"
       proved="true"
       expanded="false"
       shape="CV0aSskiptaSseqVVtaSassignVVavalid_tripleasubstV1V4V5V0V1aSifVVVtaSassertVtaSwhileVVVtFF">
@@ -412,7 +426,7 @@
      <goal
       name="WP_parameter wp.4"
       expl="parameter wp"
-      sum="1d98f58ccafb8e25b250d710e3a291d0"
+      sum="95a4085929243ddade16b291fe90bb0f"
       proved="true"
       expanded="false"
       shape="CV0aSskiptaSseqVVtaSassignVVtaSifVVVavalid_tripleaFandaFimpliesaFtermV6V9aFimpliesaFnotaFtermV6V10V0V1Iavalid_tripleV10V8V1FIavalid_tripleV9V7V1FaSassertVtaSwhileVVVtFF">
@@ -420,14 +434,14 @@
        prover="cvc3"
        timelimit="5"
        edited=""
-       obsolete="false">
+       obsolete="true">
        <result status="timeout" time="5.08"/>
       </proof>
       <proof
        prover="alt-ergo"
        timelimit="5"
        edited=""
-       obsolete="false">
+       obsolete="true">
        <result status="timeout" time="5.07"/>
       </proof>
       <proof
@@ -435,28 +449,49 @@
        timelimit="5"
        edited=""
        obsolete="false">
-       <result status="valid" time="0.78"/>
+       <result status="valid" time="0.66"/>
       </proof>
      </goal>
      <goal
       name="WP_parameter wp.5"
       expl="parameter wp"
-      sum="be14bc25a605358d0b402de18e4435bd"
+      sum="452220572080dad57c9a7e32b60ffdcb"
       proved="true"
-      expanded="false"
-      shape="CV0aSskiptaSseqVVtaSassignVVtaSifVVVtaSassertVavalid_tripleaFandV9V1V0V1aSwhileVVVtFF">
+      expanded="true"
+      shape="CV0aSskiptaSseqVVtaSassignVVtaSifVVVtaSassertVavalid_tripleaFimpliesV9V1V0V1aSwhileVVVtFF">
       <proof
        prover="coq"
        timelimit="5"
        edited="wp_total_WP_WP_WP_parameter_wp_3.v"
+       obsolete="true">
+       <result status="unknown" time="0.44"/>
+      </proof>
+      <proof
+       prover="cvc3"
+       timelimit="5"
+       edited=""
+       obsolete="false">
+       <result status="valid" time="0.04"/>
+      </proof>
+      <proof
+       prover="alt-ergo"
+       timelimit="5"
+       edited=""
        obsolete="false">
-       <result status="valid" time="0.44"/>
+       <result status="valid" time="0.05"/>
+      </proof>
+      <proof
+       prover="z3"
+       timelimit="5"
+       edited=""
+       obsolete="false">
+       <result status="valid" time="0.05"/>
       </proof>
      </goal>
      <goal
       name="WP_parameter wp.6"
       expl="parameter wp"
-      sum="ec411b6472a60f81d2c3076de8bba26e"
+      sum="457c7d860257e025ced48c9fdd71eee2"
       proved="false"
       expanded="true"
       shape="CV0aSskiptaSseqVVtaSassignVVtaSifVVVtaSassertVtaSwhileVVVavalid_tripleaFandV11aFandaFimpliesaFandaFtermV10V11V13aFimpliesaFandaFnotaFtermV10V11V1V0V1Iavalid_tripleV13V12V11FFF">
@@ -464,21 +499,21 @@
        prover="cvc3"
        timelimit="5"
        edited=""
-       obsolete="false">
+       obsolete="true">
        <result status="timeout" time="5.08"/>
       </proof>
       <proof
        prover="alt-ergo"
        timelimit="5"
        edited=""
-       obsolete="false">
+       obsolete="true">
        <result status="timeout" time="5.08"/>
       </proof>
       <proof
        prover="z3"
        timelimit="5"
        edited=""
-       obsolete="false">
+       obsolete="true">
        <result status="timeout" time="5.07"/>
       </proof>
      </goal>

examples/hoare_logic/wp_total/wp_total_Imp_assert_rule_ext_1.v

+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import ZArith.
+Require Import Rbase.
+Inductive datatype  :=
+  | Tint : datatype 
+  | Tbool : datatype .
+
+Inductive operator  :=
+  | Oplus : operator 
+  | Ominus : operator 
+  | Omult : operator 
+  | Ole : operator .
+
+Definition ident  := Z.
+
+Inductive term  :=
+  | Tconst : Z -> term 
+  | Tvar : Z -> term 
+  | Tderef : Z -> term 
+  | Tbin : term -> operator -> term -> term .
+
+Inductive fmla  :=
+  | Fterm : term -> fmla 
+  | Fand : fmla -> fmla -> fmla 
+  | Fnot : fmla -> fmla 
+  | Fimplies : fmla -> fmla -> fmla .
+
+Definition implb(x:bool) (y:bool): bool := match (x,
+  y) with
+  | (true, false) => false
+  | (_, _) => true
+  end.
+
+Inductive value  :=
+  | Vint : Z -> value 
+  | Vbool : bool -> value .
+
+Parameter map : forall (a:Type) (b:Type), Type.
+
+Parameter get: forall (a:Type) (b:Type), (map a b) -> a -> b.
+
+Implicit Arguments get.
+
+Parameter set: forall (a:Type) (b:Type), (map a b) -> a -> b -> (map a b).
+
+Implicit Arguments set.
+
+Axiom Select_eq : forall (a:Type) (b:Type), forall (m:(map a b)),
+  forall (a1:a) (a2:a), forall (b1:b), (a1 = a2) -> ((get (set m a1 b1)
+  a2) = b1).
+
+Axiom Select_neq : forall (a:Type) (b:Type), forall (m:(map a b)),
+  forall (a1:a) (a2:a), forall (b1:b), (~ (a1 = a2)) -> ((get (set m a1 b1)
+  a2) = (get m a2)).
+
+Parameter const: forall (b:Type) (a:Type), b -> (map a b).
+
+Set Contextual Implicit.
+Implicit Arguments const.
+Unset Contextual Implicit.
+
+Axiom Const : forall (b:Type) (a:Type), forall (b1:b) (a1:a), ((get (const(
+  b1):(map a b)) a1) = b1).
+
+Definition env  := (map Z value).
+