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Theorem dups-eqsize-ls
∀ key. key ∈ ks → key.dentry?, ∀ key. key.dentry? → (key ∈ ks ↔ mklink(key.ino, key.name) ∈ ls) ⊦ # ks = # ls ↔ 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: 15
Proof steps: 36
Used lemmas:
Used spec theorems:
set-basic
/alink-set/
Extension
set-basic
/node-index/
Extension
set-basic
/node-index/
indef
set-basic
/alink-set/
indef
Used simplifier rules:
set-basic
/alink-set/
size-zero
set-basic
/node-index/
Size-empty
set-basic
/alink-set/
In-empty
set-basic
/node-index/
size-zero
set-basic
/node-index/
In-empty
set-basic
/node-index/
In-insert
set-basic
/node-index/
Size-insert
set-basic
/alink-set/
size-zero-01
set-basic
/alink-set/
ne-01
key
/
elim-03
set-basic
/alink-set/
In-insert
nat-basic
/
oz
nat-basic
/
eq-01
set-basic
/alink-set/
ne
set-basic
/alink-set/
Size-insert
nat-basic
/
s-04
nat-basic
/
ref
nat-basic
/
a
nat-basic
/
c
set-basic
/node-index/
size-zero-01
set-basic
/node-index/
ne-01
key
/
sel-01
key
/
sel-02
key
/
test-01
alink
/
inj
key
/
inj-01