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Theorem lexicographic-suffix-next
⊦ n0 < # ar ∧ n1 < # ar → (suffix(ar, n0) < suffix(ar, n1) ↔ ar[n0] < ar[n1] ∨ suffix(ar, n0 + 1) < suffix(ar, n1 + 1) ∧ ar[n0] = ar[n1])
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
lrs
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 26
Proof steps: 59
Used lemmas:
ls-at-subarray
,
lexicographic
,
suffix
,
Used spec theorems:
nat-basic2
/
addex
array-copy
/
subarray-subarray-elim
array
/gearray/
Extension
array-copy
/
at-subarray
Used simplifier rules:
nat-basic2
/
l-07
nat-basic2
/
eqs
nat-basic2
/
neq-01
nat
/
le-sum
nat
/
l-num-06
nat
/
eq-add2n-1-eq-le
nat
/
neq-add1
nat-basic1
/gearray/
zero
oelem
/
transitivity
oelem
/
sls
nat-basic1
/gearray/
zero-01
nat-basic2
/
one
array-copy
/
subarray-zero
nat
/
ls-03
oelem
/
lel
nat
/
lez
nat-basic1
/gearray/
one-01
oelem
/
irreflexivity
nat-basic2
/
eq-01
nat
/
le-add
nat
/
eqle-one
oelem
/
nen
nat-basic2
/
ax-08
nat
/
lep
nat
/
ler
nat-basic2
/
l-02
nat
/
fle-01
nat
/
ls
nat-basic2
/
succ
nat
/
le-ls-simp
nat-basic1
/gearray/
lf-02
nat
/
fle
nat-basic1
/gearray/
trans-1
nat-basic1
/gearray/
lf
nat-basic1
/gearray/
neq-01
nat
/
add-01
nat
/
eq-02
nat
/
lels-02
nat
/
let
nat
/
eq
nat-basic2
/
oz
nat
/
elim-pred-c
nat
/
cancel-01
nat-basic1
/gearray/
ref-1
nat-basic2
/
l-01
nat-basic1
/gearray/
ls-03
nat-basic2
/
l
nat-basic1
/gearray/
lf-01
nat
/
lels-03
nat-basic1
/gearray/
f
nat-basic2
/
s
nat
/
succ-01
nat
/
ls-le-simp
nat-basic2
/
c
nat-basic2
/
a
nat
/
lep-02
nat
/
le
nat
/
ls-01
nat
/
ax-02
nat
/
ls-02
nat-basic1
/gearray/
ls-02
nat
/
lels-01
nat
/
lels
array-copy
/
size-subarray
array-copy
/
subarray-elim
nat
/
elim-sub