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Theorem sar-elems-bagle-twice-same
⊦ sar .elems = bag< # sar ∧ n < # sar ∧ m < # sar → (sar[n] = sar[m] ↔ n = m)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp,
Comment:
Used by:
valid-sar-twice-same
,
Used by units in proved state:
suffix-array-ops
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 31
Used lemmas:
bagle-count
,
sar-elems-bagle-size
,
Used spec theorems:
bag-array
/suffix-array-base/
ar-elems-extract1
array-copy
/suffix-array-base/
at-subarray
array-copy
/suffix-array-base/
subarray-subarray-elim
Used simplifier rules:
bag-basic
/suffix-array-base/
count-same
nat
/
ge
nat
/
not-zero
nat
/
lep
nat
/
le-num-01
nat
/
lep-02
nat-basic2
/
eq
nat
/
add-num-03
nat-basic2
/
neq-01
nat-basic2
/
succ-03
nat-basic1
/
ref-1
nat
/
ler
nat-basic2
/
ax-08
nat-basic2
/
one
nat-basic2
/
eq-01
nat
/
prop-07
nat
/
eq-02
nat
/
ls-03
nat-basic1
/
lf-02
bag-union
/suffix-array-base/
union-com
bag-union
/suffix-array-base/
union-ass
bag-union
/suffix-array-base/
union-rec
nat
/
le-ls-simp
nat
/
ls-01
nat
/
ls-02
nat
/
succ-01
nat-basic1
/
neq-01
array-copy
/suffix-array-base/
size-subarray
nat-basic2
/
l-01
nat
/
fle
nat
/
lels
nat-basic2
/
l-02
nat-basic2
/
s
nat-basic2
/
one-03
nat-basic2
/
oz
nat-basic1
/
one
nat-basic2
/
l
nat-basic1
/
lf-01
nat-basic2
/
c
nat-basic2
/
a
nat
/
lels-03
nat-basic1
/
ls-02
nat
/
lels-01
array-copy
/suffix-array-base/
subarray-elim
nat
/
elim-sub
nat
/
zero-01
nat
/
elim-pred-c
nat-basic2
/
succ
nat-basic1
/
trans-1
nat-basic1
/
lf
nat-basic1
/
f