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Theorem correctness-lrs
# ar ≠ 0 ⊦ ⟪lrs#(ar; n0, n1)⟫ ∃ n2. lrs(ar, n1, n2, n0)
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: 16
Proof steps: 62
Used lemmas:
inv
,
lrs
,
Used spec theorems:
suffix-array-ops
/
correctness-create_suffixarray
lcp
/
lcp-correct
suffix-array
/
valid-sar-index-exists
lrs
/
suffix-lcp
suffix-array
/
valid-suffix-ls
suffix-array
/
valid-sar-size
lcp
/
lcp-sym
Used simplifier rules:
nat
/
les
nat
/
eqle-one
nat-basic2
/
eq
nat
/
succ-01
nat
/
le-one
suffix-array
/
valid-sar-twice-same
nat-basic1
/
zero-01
lcp
/
lcp-end-right1
nat
/
anti
suffix-array
/
valid-sar-at-le
nat-basic1
/
ref-1
nat
/
le-add
nat
/
le-num-02
nat
/
l-num-01
nat
/
add-num-03
nat
/
ls-le-simp
nat-basic2
/
l
nat-basic2
/
oz
nat
/
elim-pred-c
nat
/
lep-02
nat
/
le
nat-basic1
/
ls-02
nat
/
ls-01
suffix-array
/
valid-sar-at-ls
nat
/
lels
nat-basic1
/
lf-02
nat-basic1
/
lf-01
nat
/
fle
nat-basic1
/
lf
nat-basic1
/
trans-1
nat
/
let
nat
/
fle-01
suffix-array
/
valid-sar-twice-same1
nat-basic2
/
s
nat-basic2
/
succ
nat
/
le-ls-simp
nat
/
lels-03
nat-basic1
/
f
nat
/
ler
lcp
/
lcp-end-right
nat
/
not-zero
nat-basic1
/
one-01
nat
/
lels-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
l-02
nat-basic1
/
zero
suffix-array
/
valid-sar-size
lrs
/
rs
lrs
/
lrs
nat
/
ax-02