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Theorem dls-split
# x0 = # rx0, # x1 = # rx1, x0 ≠ [], x1 ≠ [] ⊦ dls(head, prev, x0 + a ' + x1, rx0 + r ' + rx1, next, tail) = _∃(λ r0, r1. dls(head, prev, x0, rx0, r, r0) * r => mkcell(r0, r1, a) * dls(r1, r, x1, rx1, next, tail))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
implementation
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 37
Used lemmas:
dls-emp
,
dls-one
,
dls-rec
,
Used spec theorems:
heap-sep
/cell-heap/
Eq-P
Used simplifier rules:
maplet
/cell-heap/
ex2-shift
list-data
/reflist/
size-01
nat-basic2
/
oz
maplet
/cell-heap/
eq-objs
list
/reflist/
app
list
/
app
list
/
e-01
list
/
len-02
list
/
len
list
/
c
list-data
/reflist/
elim-list-c
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
eq-01
list
/reflist/
len-02
list
/reflist/
len
list
/reflist/
c
maplet
/cell-heap/
ex1-shift
heap-sep
/cell-heap/
true-and
list
/reflist/
c-07
heap-sep
/cell-heap/
true-rev
list
/reflist/
c-08
list
/reflist/
e-01
list
/reflist/
Nil
list
/
Nil
heap-sep
/cell-heap/
prop
heap-sep
/cell-heap/
and
heap-sep
/cell-heap/
and-com
heap-sep
/cell-heap/
and-ass
heap-sep
/cell-heap/
emp-sep
heap-sep
/cell-heap/
prop-shift
list-data
/reflist/
l
list-data
/
size-01
list
/reflist/
a
list
/
a
heap-sep
/cell-heap/
sep-com
heap-sep
/cell-heap/
sep-ass