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Theorem entries-dom
⊦ ((abs(sdt, sdi) * D))(dirs) → (str ∈ sdi ↔ str ∈ sdt)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
entries-dom1
,
entries-dom2
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 9
Used lemmas:
abs-empty
,
entries-any
,
Used spec theorems:
directory-tree-base
/
In-insert
store
/dir-entries/
In-insert
Used simplifier rules:
directory-tree-base
/
In-empty
heap-sep
/dir-heap/
prop-shift
heap-sep
/dir-heap/
emp-sep
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
store
/directory-tree-inst/
neq
heap-sep
/dir-heap/
sep-ass
heap-sep
/dir-heap/
sep-com
directory-tree-base
/
Size-insert
nat-basic
/
s-04
oelem
/nat-set/
irreflexivity
nat-basic
/
a
nat-basic
/
c