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Theorem dups-eqsize-entries
∀ key. key ∈ ks → key.dentry? ∧ key.ino = ino, ∀ key. key.dentry? ∧ key.ino = ino → (key ∈ ks ↔ key.name ∈ entries) ⊦ # ks = # entries ↔ true
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 31
Used lemmas:
Used spec theorems:
store
/dir-entries/
k-Extension
set-basic
/node-index/
Extension
set-basic
/node-index/
indef
store
/dir-entries/
exin
Used simplifier rules:
store
/dir-entries/
empty
set-basic
/node-index/
Size-empty
store
/dir-entries/
In-empty
set-basic
/node-index/
size-zero
set-basic
/node-index/
size-zero-01
set-basic
/node-index/
In-empty
set-basic
/node-index/
In-insert
nat-basic
/
oz
key
/
elim-03
key
/
sel-01
key
/
sel-02
key
/
test-01
nat-basic
/
eq-01
store
/dir-entries/
Size-insert
set-basic
/node-index/
Size-insert
nat-basic
/
s-04
nat-basic
/
ref
nat-basic
/
a
nat-basic
/
c
store
/dir-entries/
In-insert
key
/
inj-01