diff --git a/examples/DetOperations.curry b/examples/DetOps.curry
similarity index 100%
rename from examples/DetOperations.curry
rename to examples/DetOps.curry
diff --git a/examples/Proof-last-is-deterministic.agda b/examples/Proof-DetOps-last-is-deterministic.agda
similarity index 97%
rename from examples/Proof-last-is-deterministic.agda
rename to examples/Proof-DetOps-last-is-deterministic.agda
index e704334ca1e2c4189a3eeb8019b28623b8ab0ff9..d433c6f8db5d96b37b3f5b5eeb9bbd1ece1266d3 100644
--- a/examples/Proof-last-is-deterministic.agda
+++ b/examples/Proof-DetOps-last-is-deterministic.agda
@@ -1,4 +1,4 @@
-module Proof-last-is-deterministic where
+module Proof-DetOps-last-is-deterministic where
 
 -- Show that last is a deterministic operation.
 -- The property to show is:
diff --git a/examples/withVerification/PROOF-appendAddLengths.agda b/examples/withVerification/PROOF-ListProp-appendAddLengths.agda
similarity index 95%
rename from examples/withVerification/PROOF-appendAddLengths.agda
rename to examples/withVerification/PROOF-ListProp-appendAddLengths.agda
index 5294fa52d2ede43be95445194e5d3a6b5420f42b..69f36087ae14182a824ac5ea9e5bef36861cb08a 100644
--- a/examples/withVerification/PROOF-appendAddLengths.agda
+++ b/examples/withVerification/PROOF-ListProp-appendAddLengths.agda
@@ -2,7 +2,7 @@
 
 open import bool
 
-module PROOF-appendAddLengths
+module PROOF-ListProp-appendAddLengths
   (Choice : Set)
   (choose : Choice → 𝔹)
   (lchoice : Choice → Choice)
diff --git a/examples/withVerification/PROOF-sortPreservesLength.agda b/examples/withVerification/PROOF-SortSpec-sortPreservesLength.agda
similarity index 96%
rename from examples/withVerification/PROOF-sortPreservesLength.agda
rename to examples/withVerification/PROOF-SortSpec-sortPreservesLength.agda
index 1e75a12d9d1821a5bc73ae8844ad46d693e717f6..5204f93250f8c72cf5a014600315227d262dffae 100644
--- a/examples/withVerification/PROOF-sortPreservesLength.agda
+++ b/examples/withVerification/PROOF-SortSpec-sortPreservesLength.agda
@@ -2,7 +2,7 @@
 
 open import bool
 
-module PROOF-sortPreservesLength
+module PROOF-SortSpec-sortPreservesLength
   (Choice : Set)
   (choose : Choice → 𝔹)
   (lchoice : Choice → Choice)
diff --git a/examples/withVerification/README b/examples/withVerification/README
index 4bec2ae66c3e0f8a159bfaf16b2bd2d1581160b4..2090e2bebcd7d83f69fc384808490350266650cb 100644
--- a/examples/withVerification/README
+++ b/examples/withVerification/README
@@ -4,8 +4,8 @@ Combining Testing and Verification
 This directory contains some examples demonstrating the
 combination of testing and verification.
 
-If there are is a property `p` in a program for which
-a proof exists, i.e., a file named `proof-p` (the name
+If there are is a property `p` in a program `m` for which
+a proof exists, i.e., a file named `proof-m-p` (the name
 is case independent), then:
 
 1. Property `p` is not checked by CurryCheck
@@ -31,7 +31,7 @@ To do so, we first formulate it as a property:
 
 To get some confidence in its general correctness, we test it:
 
-    > curry check ListProp
+    > curry-check ListProp
     ...
     Executing all tests...
     appendAddLengths_ON_BASETYPE (module ListProp, line 14):
@@ -46,17 +46,17 @@ functions into an Agda program:
     > curry2verify ListProp
     ...
     Agda module 'TO-PROVE-appendAddLengths.agda' written.
-    If you completed the proof, rename it to 'PROOF-appendAddLengths.agda'.
+    ...
 
 Now, we complete the Agda program `TO-PROVE-appendAddLengths.agda`
 by a straightforward induction on the first argument of `appendAddLengths`.
 
 Since the proof is complete, we rename the Agda module into
-`PROOF-appendAddLengths.agda`.
+`PROOF-ListProp-appendAddLengths.agda`.
 
 To see the effect of this proof for program testing, we run CurryCheck again:
 
-    > curry check ListProp
+    > curry-check ListProp
     Analyzing module 'ListProp'...
     >
 
@@ -65,7 +65,7 @@ Hence, CurryCheck does not perform any test since the property
 simplify the postcondition to `True` so that it trivially holds.
 This simplification process can be visualized with option `-v`:
 
-    > curry check ListProp -v
+    > curry-check ListProp -v2
     Analyzing module 'ListProp'...
     ...
     POSTCONDITION: append'post(a, b, c) → ==(+(length(a), length(b)), length(c))
diff --git a/examples/withVerification/SortSpec.curry b/examples/withVerification/SortSpec.curry
index 73910f304f3d3cdf18530608c569e597f3daf4f0..130ddf5f584342917ce63b6a0d64fd1abfaa1b15 100644
--- a/examples/withVerification/SortSpec.curry
+++ b/examples/withVerification/SortSpec.curry
@@ -26,7 +26,8 @@ sort'post xs ys = length xs == length ys && sorted ys
 -- Specification of sort:
 -- A list is a sorted result of an input if it is a permutation and sorted.
 sort'spec :: [Int] -> [Int]
-sort'spec xs | ys == perm xs && sorted ys = ys  where ys free
+sort'spec xs | sorted ys = ys
+ where ys = perm xs
 
 -- An implementation of sort with quicksort:
 sort :: [Int] -> [Int]
diff --git a/package.json b/package.json
index 080a768c223f359d22f40c4496285c1a77de2eab..4de7993cea9041209438b647e54ceab63cb8e3eb 100644
--- a/package.json
+++ b/package.json
@@ -20,7 +20,7 @@
     },
     "testsuite": [
         { "src-dir": "examples",
-          "modules": [ "DefaultRulesTest", "DetOperations", "ExampleTests",
+          "modules": [ "DefaultRulesTest", "DetOps", "ExampleTests",
                        "ExamplesFromManual", "FloatTest", "ListSpecifications",
                        "Nats", "SEBF", "Sum", "SortSpec", "Tree" ]
         },
diff --git a/src/CurryCheck.curry b/src/CurryCheck.curry
index c0fb182bb8f9390ce64646f5d607fbb660354f8a..107e6a4e18db2c0935750456eb8ad52fdcda7d0b 100644
--- a/src/CurryCheck.curry
+++ b/src/CurryCheck.curry
@@ -30,8 +30,9 @@ import AbstractCurry.Types
 import AbstractCurry.Files
 import AbstractCurry.Select
 import AbstractCurry.Build
-import AbstractCurry.Pretty    (showCProg)
-import AbstractCurry.Transform (renameCurryModule,updCProg,updQNamesInCProg)
+import AbstractCurry.Pretty    ( showCProg )
+import AbstractCurry.Transform ( renameCurryModule, updCProg
+                               , updQNamesInCProg, updQNamesInCFuncDecl )
 import qualified FlatCurry.Types as FC
 import FlatCurry.Files
 import qualified FlatCurry.Goodies as FCG
@@ -51,7 +52,7 @@ ccBanner :: String
 ccBanner = unlines [bannerLine,bannerText,bannerLine]
  where
    bannerText = "CurryCheck: a tool for testing Curry programs (Version " ++
-                packageVersion ++ " of 08/10/2018)"
+                packageVersion ++ " of 30/10/2018)"
    bannerLine = take (length bannerText) (repeat '-')
 
 -- Help text
@@ -387,14 +388,14 @@ classifyTests opts prog = map makeProperty
 
 -- Extracts all tests from a given Curry module and transforms
 -- all polymorphic tests into tests on a base type.
+-- The third argument contains the list of function representing
+-- proved properties. It is used to simplify post conditions to be tested.
 -- The result contains a triple consisting of all actual tests,
 -- all ignored tests, and the public version of the original module.
-transformTests :: Options -> String -> CurryProg
+transformTests :: Options -> String -> [CFuncDecl] -> CurryProg
                -> IO ([CFuncDecl],[CFuncDecl],CurryProg)
-transformTests opts srcdir
+transformTests opts srcdir theofuncs
                prog@(CurryProg mname imps typeDecls functions opDecls) = do
-  theofuncs <- if optProof opts then getTheoremFunctions srcdir prog
-                                else return []
   simpfuncs <- simplifyPostConditionsWithTheorems (optVerb opts) theofuncs funcs
   let preCondOps  = preCondOperations simpfuncs
       postCondOps = map ((\ (mn,fn) -> (mn, fromPostCondName fn)) . funcName)
@@ -541,13 +542,13 @@ revertDetOpTrans detops fdecl@(CFunc qf@(mn,fn) ar vis texp _) =
 -- for f.
 genDetOpTests :: [String] -> [QName] -> [CFuncDecl] -> [CFuncDecl]
 genDetOpTests prooffiles prefuns fdecls =
-  map (genDetProp prefuns) (filter isDetOrgOp fdecls)
+  map (genDetProp prefuns) (filter (isDetOrgOp . funcName) fdecls)
  where
-  isDetOrgOp fdecl =
-   let fn = snd (funcName fdecl)
-    in "_ORGNDFUN" `isSuffixOf` fn &&
-       not (existsProofFor (determinismTheoremFor (take (length fn - 9) fn))
-                           prooffiles)
+  isDetOrgOp (mn,fn) =
+    "_ORGNDFUN" `isSuffixOf` fn &&
+    not (existsProofFor (mnorg, determinismTheoremFor (take (length fn - 9) fn))
+                        prooffiles)
+   where mnorg = take (length mn - 10) mn -- remove _PUBLICDET suffix
 
 -- Transforms a declaration of a deterministic operation f_ORGNDFUN
 -- into a determinisim property test of the form
@@ -668,9 +669,16 @@ analyseCurryProg opts modname orgprog = do
   let words      = map firstWord (lines progtxt)
       staticerrs = missingCPP ++ map (showOpError words) staticoperrs
   putStrIfDetails opts "Generating property tests...\n"
+  theofuncs <- if optProof opts then getTheoremFunctions srcdir prog
+                                else return []
+  -- compute already proved theorems for public module:
+  let pubmodname = modname++"_PUBLIC"
+      rnm2pub mn@(mod,n) | mod == modname = (pubmodname,n)
+                         | otherwise      = mn
+      theopubfuncs = map (updQNamesInCFuncDecl rnm2pub) theofuncs
   (rawTests,ignoredTests,pubmod) <-
-        transformTests opts srcdir . renameCurryModule (modname++"_PUBLIC")
-                                   . makeAllPublic $ prog
+        transformTests opts srcdir theopubfuncs
+          . renameCurryModule pubmodname . makeAllPublic $ prog
   let (rawDetTests,ignoredDetTests,pubdetmod) =
         transformDetTests opts prooffiles
               . renameCurryModule (modname++"_PUBLICDET")
diff --git a/src/SimplifyPostConds.curry b/src/SimplifyPostConds.curry
index 12c017f66ad5288d1ed86ce013ab876d7dfe96b4..edac492762f671aa0a99343308e0bb698c8b92a3 100644
--- a/src/SimplifyPostConds.curry
+++ b/src/SimplifyPostConds.curry
@@ -31,7 +31,6 @@ import Rewriting.Substitution
 import Rewriting.Rules
 
 import ContractUsage
-import TheoremUsage
 
 -- Simplify the postconditions contained in the third argument w.r.t. a given
 -- list of theorems (second argument).
diff --git a/src/TheoremUsage.curry b/src/TheoremUsage.curry
index 1a938dd5d51d1e16d9c56bbf56a8da8818873be8..fee42ec622e0f2ac490523446fe150aa06570a0e 100644
--- a/src/TheoremUsage.curry
+++ b/src/TheoremUsage.curry
@@ -9,18 +9,19 @@
 ---
 --- * A theorem is considered as proven and, thus, not be checked
 ---   by CurryCheck or the contract wrapper (see `currypp`), if there exists
----   a file named with prefix "Proof" and the name of the theorem, e.g.,
----   `Proof-sortPreservesLength.agda`. The name is not case sensitive,
----   the file name extension is arbitrary and the special characters in the
----   name are ignored. Hence, a proof for `sortlength` could be also stored in
----   a file named `PROOF_sort-perserves-length.smt`.
+---   a file named with prefix "Proof" and the qualified name of the theorem,
+---    e.g., `Proof-Sort-sortPreservesLength.agda`.
+---   The name is not case sensitive, the file name extension is arbitrary
+---   and the special characters in the name are ignored.
+---   Hence, a proof for `sortlength` could be also stored in
+---   a file named `PROOF_Sort_sort_preserves_length.smt`.
 ---
 ---  * A proof that some operation `f` is deterministic has the name
 ---    `fIsDeterministic` so that a proof for `last` can be stored in
 ---    `proof-last-is-deterministic.agda` (and also in some other files).
 ---
 --- @author Michael Hanus
---- @version August 2016
+--- @version October 2018
 ------------------------------------------------------------------------
 
 module TheoremUsage
@@ -56,20 +57,20 @@ getProofFiles dir = do
   return (filter isProofFileName files)
 
 --- Does the list of file names (second argument) contain a proof of the
---- theorem given as the first argument?
-existsProofFor :: String -> [String] -> Bool
-existsProofFor propname filenames =
-  any (isProofFileNameFor propname) filenames
+--- qualified theorem name given as the first argument?
+existsProofFor :: QName -> [String] -> Bool
+existsProofFor qpropname filenames =
+  any (isProofFileNameFor qpropname) filenames
 
 --- Is this a file name with a proof, i.e., start it with `proof`?
 isProofFileName :: String -> Bool
 isProofFileName fn = "proof" `isPrefixOf` (map toLower fn)
 
 --- Is this the file name of a proof of property `prop`?
-isProofFileNameFor :: String -> String -> Bool
-isProofFileNameFor prop fname =
+isProofFileNameFor :: QName -> String -> Bool
+isProofFileNameFor (mn,prop) fname =
   let lfname = map toLower (dropExtension fname)
-      lprop  = map toLower prop
+      lprop  = map toLower (mn ++ prop)
    in if "proof" `isPrefixOf` lfname
       then deleteNonAlphanNum (drop 5 lfname) == deleteNonAlphanNum lprop
       else False
@@ -86,7 +87,7 @@ getTheoremFunctions :: String -> CurryProg -> IO [CFuncDecl]
 getTheoremFunctions proofdir (CurryProg _ _ _ functions _) = do
   let propfuncs = filter isProperty functions -- all properties
   prooffiles <- getProofFiles proofdir
-  return $ filter (\fd -> existsProofFor (snd (funcName fd)) prooffiles)
+  return $ filter (\fd -> existsProofFor (funcName fd) prooffiles)
                   propfuncs
 
 ------------------------------------------------------------------------