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Theorem at-del
p ≠ ε, q ∈ tree -- p ⊦ p ∈ tree → (tree -- p)[q] = (q ⊑ p ⊃ tree[q] -- restn(# q, p);tree[q])
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
posix-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 14
Used lemmas:
one-inf
,
del-recin
,
at-dnode
,
nil-in
,
del-here
,
split-at
,
nil-at
,
one-at
,
one-ind
,
in-del
,
split-in
,
Used spec theorems:
Used simplifier rules:
list-data
/path/
size-01
list-del
/path/
restN-zero
nat-basic
/
c
nat-basic
/
a
list-del
/path/
weak-restN-rec
nat-basic
/
succ
list
/path/
len-05
list
/path/
c
list-last
/path/
prefix-nil
directory-tree-base
/
Del-at
list
/path/
e-01
list-last
/path/
prefix-one-01
store
/directory-tree-inst/
Del-at-strong
directory-tree-base
/
Del-in
list
/path/
app
list
/path/
c-03
store
/directory-tree-inst/
in-neq
directory-tree-base
/
At-other
list-last
/path/
prefix-rec-03
store
/directory-tree-inst/
insin
list
/path/
a
list-last
/path/
prefix-rec-02
directory-tree-base
/
At-same
directory-tree-base
/
In-insert