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Theorem ll-trav1-end
r1 ≠ null ⊦ h(r1) = a × null → ((ll-trav(r0, r1, x) * hP)(h) ↔ x ≠ [] ∧ (∃ y. x = y + a ∧ (lls(r0, r1, y) * r1 => a × null * hP)(h)))
Type: A user defined theorem
Validity: The proof is valid.
Features: as,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 2
Proof steps: 9
Used lemmas:
lls-one
,
lls-null
,
lls-rec
,
lls-base
,
ll-trav1-def
,
Used spec theorems:
Used simplifier rules:
list
/
Last
map-sep
/
sep-com
map-sep
/
sep-ass
list
/
a
list
/
app-02
map-sep
/
false-rev
map-sep
/
false-and
map-sep
/
and-ass
map-sep
/
and-com
map-sep
/
false-sep
map-sep
/
falseH
list
/
e
refmap-maplet
/
ex1-shift
refmap-maplet
/
at-rw
cell
/
inj-tim
list
/
c
map-sep
/
true-rev
map-sep
/
true-and
map-sep
/
emp-sep
map-sep
/
prop-shift
map-sep
/
and
map-sep
/
prop
list
/
app
list
/
len-06