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Theorem ar-elems-extract1
⊦ n < # ar → ar .elems = (subarray(ar, 0, n) .elems ∪ subarray(ar, n + 1, # ar - n - 1) .elems) ++ ar[n]
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
suffix-array
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 15
Used lemmas:
ar-elems1
,
ar-elems-append
,
elems-rec
,
elems
,
Used spec theorems:
array-splice
/
subarray-split-at
array-splice
/
subarray-split-first
Used simplifier rules:
array
/
cgetput
bag-union
/
union-rec
bag-union
/
union-empty
bag-union
/
union-ass
bag-basic
/
insert-inj
bag-union
/
union-com
array-splice
/
append-len
array
/
Size-put
array
/
Size-mkarray
array-splice
/
append-a
nat-basic1
/
ref-1
nat-basic2
/
l
nat
/
ler
nat
/
eqle-one
nat-basic2
/
ax-08
nat
/
add-01
nat
/
succ-01
nat
/
lels
nat
/
eq
nat-basic2
/
oz
nat-basic2
/
l-01
nat-basic2
/
eq-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
l-02
nat-basic2
/
s
nat-basic1
/
lf-01
nat
/
lels-03
nat-basic1
/
ls-02
nat
/
lels-01
array-copy
/
subarray-elim
nat
/
elim-sub
nat-basic1
/
f
array-copy
/
size-subarray
nat
/
zero-01
nat
/
elim-pred-c