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Theorem ls-union
⊦ h0 ⊥ h1 ∧ ls(r, x)(h0) → (((ls(r, y) * hP))(h0 ∪ h1) ↔ x = y ∧ hP(h1))
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 15
Used lemmas:
ls-rec
,
ls-null
,
ls-base
,
Used spec theorems:
maplet
/cell-heap/
map-del
heap
/cell-heap/
disj
Used simplifier rules:
heap-sep
/
split-union
heap-sep
/
sep-ass
heap-sep
/
sep-com
heap-sep
/
prop-shift
heap-sep
/
emp-sep
heap-sep
/
and
heap-sep
/
emp
heap-sep
/
prop
heap-sep
/
and-ass
heap-sep
/
and-com
heap
/cell-heap/
uni-emp-l
heap
/cell-heap/
disj-emp-l
list
/
c
maplet
/cell-heap/
ex1-shift
list
/
a
list
/
e-01
maplet
/cell-heap/
map-null
heap-sep
/
false-rev
heap-sep
/
false-sep
heap-sep
/
falseH
maplet
/cell-heap/
ex1
list
/
c-06
heap
/cell-heap/
del-uni
maplet
/cell-heap/
map-in
heap
/cell-heap/
in-uni
cell
/
inj-tim
maplet
/cell-heap/
at-eq
heap
/cell-heap/
at-uni
heap
/cell-heap/
disj-l
heap
/cell-heap/
in-del
heap
/cell-heap/
del-notin