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Theorem abs-fold-del
⊦ str ∈ entries ∧ p ∈ tree ∧ tree[p] = dnode(md, sdt) ∧ ((abs|(tree, ROOT_INO, p, ino0) * ino0 => mkdir(# entries - 1, md, m0, m1, entries -- str) * abs(sdt -- str, entries -- str)))(dirs) → abs(tree -- (p + str '), ROOT_INO)(dirs)
Type: A user defined theorem
Validity: The proof is valid.
Features: lss,
Comment:
Used by:
refine-rmdir
,
refine-unlink
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas:
abs-fold-del-p
,
Used spec theorems:
Used simplifier rules:
store
/dir-entries/
Size-empty
store
/dir-entries/
Del-empty
vfs-abs
/
entries-empty
heap-sep
/dir-heap/
prop-shift
heap-sep
/dir-heap/
and-ass
heap-sep
/dir-heap/
and-com
heap-sep
/dir-heap/
and
heap-sep
/dir-heap/
prop
store
/dir-entries/
In-empty
nat
/
elim-pred-c
store
/dir-entries/
empty
heap-sep
/dir-heap/
emp-sep
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
nat
/
add-01
nat-basic
/
add-base
nat-basic
/
a
nat-basic
/
c