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Theorem remove-insert-inverse-twice
r0 ≠ r1, r0 ∈ rx, r0 ≠ head, r0 ≠ tail, r1 ∈ rx, r1 ≠ head, r1 ≠ tail, ((dls(head, prev, x, rx, next, tail) * P))(H) ⊦ ⟪remove(r0; H); remove(r1; H); insert(r1; H); insert(r0; H)⟫ ((dls(head, prev, x, rx, next, tail) * P))(H)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 19
Used lemmas:
insert-simple-contract
,
remove-simple-contract
,
Used spec theorems:
Used simplifier rules:
list
/reflist/
in-01
list
/reflist/
in-13
nat
/
add-num-01
list
/
len-02
maplet
/cell-heap/
eq-objs
list
/reflist/
in-17
list
/reflist/
in-append
nat-basic2
/
eq-01
list-data
/reflist/
size-01
list
/reflist/
app
list-data
/
l
list-data
/reflist/
elim-list-c
list
/
len
dllist
/
dls-length
list
/reflist/
e-01
nat-basic2
/
c
nat-basic2
/
a
list
/reflist/
len-02
list
/reflist/
len
list
/reflist/
c
list
/
a
list
/reflist/
a
heap-sep
/cell-heap/
sep-ass
heap-sep
/cell-heap/
sep-com