diff --git a/spec/design/skel/X64/ArchVSpace_H.thy b/spec/design/skel/X64/ArchVSpace_H.thy
index 37bf5b98dc..f9fe9b0206 100644
--- a/spec/design/skel/X64/ArchVSpace_H.thy
+++ b/spec/design/skel/X64/ArchVSpace_H.thy
@@ -22,7 +22,7 @@ begin
 
 context Arch begin global_naming X64_H
 
-#INCLUDE_HASKELL SEL4/Kernel/VSpace/X64.lhs CONTEXT X64_H bodies_only ArchInv=ArchRetypeDecls_H NOT checkPML4At checkPDPTAt checkPDAt checkPTAt checkPML4ASIDMapMembership checkValidMappingSize asidInvalidate
+#INCLUDE_HASKELL SEL4/Kernel/VSpace/X64.lhs CONTEXT X64_H bodies_only ArchInv=ArchRetypeDecls_H NOT checkPML4At checkPDPTAt checkPDAt checkPTAt checkValidMappingSize
 #INCLUDE_HASKELL SEL4/Object/IOPort/X64.lhs CONTEXT X64_H bodies_only ArchInv=ArchRetypeDecls_H
 
 defs checkValidMappingSize_def:
diff --git a/spec/haskell/src/SEL4/Kernel/VSpace/X64.lhs b/spec/haskell/src/SEL4/Kernel/VSpace/X64.lhs
index b09452ab56..7803589a3f 100644
--- a/spec/haskell/src/SEL4/Kernel/VSpace/X64.lhs
+++ b/spec/haskell/src/SEL4/Kernel/VSpace/X64.lhs
@@ -194,16 +194,8 @@ Locating the page directory for a given ASID is necessary when updating or delet
 >     assert (pm .&. mask pml4Bits == 0)
 >         "findVSpaceForASIDAssert: pml4 pointer alignment check"
 >     checkPML4At pm
->     checkPML4UniqueToASID pm asid
->     asidMap <- gets (x64KSASIDMap . ksArchState)
->     flip assert "findVSpaceForASIDAssert: pml4 map mismatch"
->         $ case asidMap ! asid of
->             Nothing -> True
->             Just pm'-> pm == pm'
 >     return pm
 
-These checks are too expensive to run in haskell. The first funcion checks that the pointer is to a page directory, which would require testing that each entry of the table is present. The second checks that the page directory appears in x64KSASIDMap only on the ASIDs specified, which would require walking all possible ASIDs to test. In the formalisation of this specification, these functions are given alternative definitions that make the appropriate checks.
-
 > -- FIXME x64: these are all now unused.
 
 > checkPML4At :: PPtr PML4E -> Kernel ()
@@ -218,15 +210,6 @@ These checks are too expensive to run in haskell. The first funcion checks that
 > checkPTAt :: PPtr PTE -> Kernel ()
 > checkPTAt _ = return ()
 
-> checkPML4ASIDMapMembership :: PPtr PML4E -> [ASID] -> Kernel ()
-> checkPML4ASIDMapMembership _ _ = return ()
-
-> checkPML4UniqueToASID :: PPtr PML4E -> ASID -> Kernel ()
-> checkPML4UniqueToASID pd asid = checkPML4ASIDMapMembership pd [asid]
-
-> checkPML4NotInASIDMap :: PPtr PML4E -> Kernel ()
-> checkPML4NotInASIDMap pd = checkPML4ASIDMapMembership pd []
-
 \subsubsection{Locating Page Table and Page Directory Slots}
 
 The "lookupPTSlot" function locates the page table slot that maps a given virtual address, and returns a pointer to the slot. It will throw a lookup failure if the required page directory slot does not point to a page table.
@@ -456,15 +439,6 @@ This helper function checks that the mapping installed at a given PT or PD slot
 > setCurrentVSpaceRoot :: PAddr -> ASID -> Kernel ()
 > setCurrentVSpaceRoot vspace asid = setCurrentCR3 $ CR3 vspace asid
 
-> updateASIDMap :: ASID -> Kernel ()
-> updateASIDMap asid = do
->     vs <- findVSpaceForASIDAssert asid
->     asidMap <- gets (x64KSASIDMap . ksArchState)
->     let asidMap' = asidMap//[(asid, Just vs)]
->     modify (\s -> s {
->         ksArchState = (ksArchState s)
->         { x64KSASIDMap = asidMap' }})
-
 > -- FIXME x64: Currently we don't have global state for the CR3 so
 > -- we can't test whether or not we should write to it. We should
 > -- add global state to remember the CR3 and actually avoid the write/flush
@@ -480,7 +454,6 @@ This helper function checks that the mapping installed at a given PT or PD slot
 >                     capPML4BasePtr = pd }) -> do
 >                 pd' <- findVSpaceForASID asid
 >                 when (pd /= pd') $ throw InvalidRoot
->                 withoutFailure $ updateASIDMap asid
 >                 curCR3 <- withoutFailure $ getCurrentCR3
 >                 when (curCR3 /= CR3 (addrFromPPtr pd) asid) $
 >                         withoutFailure $ setCurrentCR3 $ CR3 (addrFromPPtr pd) asid
@@ -547,19 +520,9 @@ Note that implementations with separate high and low memory regions may also wis
 
 \subsection{Managing ASID Map}
 
-> invalidateASID' :: ASID -> Kernel ()
-> invalidateASID' asid = do
->     findVSpaceForASIDAssert asid
->     asidMap <- gets (x64KSASIDMap . ksArchState)
->     let asidMap' = asidMap//[(asid, Nothing)]
->     modify (\s -> s {
->         ksArchState = (ksArchState s)
->         { x64KSASIDMap = asidMap' }})
-
 > invalidateASIDEntry :: ASID -> PPtr PML4E -> Kernel ()
-> invalidateASIDEntry asid vspace = do
+> invalidateASIDEntry asid vspace =
 >     doMachineOp $ hwASIDInvalidate (fromPPtr vspace) (fromASID asid)
->     invalidateASID' asid
 
 \subsection{Decoding x64 Invocations}
 
diff --git a/spec/haskell/src/SEL4/Model/StateData/X64.lhs b/spec/haskell/src/SEL4/Model/StateData/X64.lhs
index 03649998f0..f4bcadfa8f 100644
--- a/spec/haskell/src/SEL4/Model/StateData/X64.lhs
+++ b/spec/haskell/src/SEL4/Model/StateData/X64.lhs
@@ -35,7 +35,6 @@ This module contains the architecture-specific kernel global data for the X86-64
 
 > data KernelState = X64KernelState {
 >     x64KSASIDTable   :: Array ASID (Maybe (PPtr ASIDPool)),
->     x64KSASIDMap     :: Array ASID (Maybe (PPtr PML4E)),
 >     x64KSGlobalPML4  :: PPtr PML4E,
 >     x64KSGlobalPDPTs :: [PPtr PDPTE],
 >     x64KSGlobalPDs   :: [PPtr PDE],