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Theorem sorted-lt-h
⊦ m0 < m ∧ m1 < m ∧ sorted(zbrar, n, m) → (zbrar[n + m0].key < zbrar[n + m1].key ↔ m0 < m1)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
sorted-all
,
sorted-lt
,
sorted-lt-post
,
sorted-lt-pre
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 17
Used lemmas:
sorted-rec
,
sorted-one
,
sorted-base
,
Used spec theorems:
Used simplifier rules:
nat
/
lels
nat
/
lez-01
nat-basic
/
f
oelem
/key-order/
ls-le
nat-basic
/
zero
oelem
/key-order/
irreflexivity
oelem
/key-order/
transitivity
nat
/
lep-02
nat-basic
/
s-04
nat-basic
/
succ
oelem
/key-order/
nll
nat
/
lez
nat-basic
/
zero-01
nat-basic
/
add-base
nat
/
le-ls-simp
nat-basic
/
a
nat-basic
/
c