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Theorem transitivity
⊦ key < key0 ∧ key0 < key1 → key < key1
Type: A proof obligation
Validity: The proof is valid.
Features:
Comment: |- a < b and b < c -> a < c
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 22
Proof steps: 37
Used lemmas:
Used spec theorems:
key-order-def
/
inode-less
key-order-def
/
datakey-less
key-order-def
/
dentrykey-less
Used simplifier rules:
key-order-def
/
inode-less
key
/
test-02
nat-basic
/
succ
nat-basic
/
l-02
nat-basic
/
a
nat-basic
/
c
key
/
test-04
key
/
test-06
key
/
disjpred-05
key
/
disjpred-03
key-order-def
/
datakey-less
key
/
sel-05
nat-basic
/
trans
nat
/
ls-le-simp
nat
/
lels
key-order-def
/
dentrykey-less
nat
/
fle-01
key
/
test-08
key
/
test-05
key
/
sel-04
key
/
test-09
key
/
test-03
key
/
sel-03
key
/
test-07
key
/
sel-01
key
/
test-01
key
/
sel-02
nat
/
le-ls-simp
key
/
disjpred-06
key
/
disjpred-04
string-less
/
Transitivity
nat
/
fle
nat-basic
/
f
nat-basic
/
ls-02
nat-basic
/
lf-02
nat-basic
/
lf-01
nat-basic
/
ref
nat
/
lels-02
nat-basic
/
lf