[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem remove-insert-inverse
r ∈ rx, r ≠ head, r ≠ tail, ((dls(head, prev, x, rx, next, tail) * P))(H) ⊦ ⟪remove(r; H); insert(r; 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: 3
Proof steps: 9
Used lemmas:
insert-simple-contract
,
remove-simple-contract
,
Used spec theorems:
Used simplifier rules:
nat-basic2
/
eq-01
list
/reflist/
in-13
list-data
/reflist/
size-01
list-data
/
l
list-data
/reflist/
elim-list-c
nat
/
add-num-01
nat-basic2
/
c
nat-basic2
/
a
list
/
len-02
list
/
len
dllist
/
dls-length
list
/reflist/
e-01
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