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Theorem subarray-inc-offset0
m + n ≤ # ar, n ≠ 0 ⊦ subarray(ar, m, n) = ar[m] + subarray(ar, m + 1, n - 1)
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: 5
Proof steps: 15
Used lemmas:
subarray-inc
,
Used spec theorems:
array
/
Extension
list-del
/list-as-arrayinstance/
get-append-less
array-copy
/
at-subarray
Used simplifier rules:
list
/list-as-arrayinstance/
c
nat
/
elim-pred-c
list-data
/list-as-arrayinstance/
l
nat-basic
/
f
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
list
/list-as-arrayinstance/
Last
nat
/
le-ls-simp
nat
/
lels
nat-basic
/
oz
nat-basic
/
s-04
list
/list-as-arrayinstance/
a
list
/list-as-arrayinstance/
len-02
array-copy
/
size-subarray
list
/list-as-arrayinstance/
len
nat-basic
/
eq-01
nat-basic
/
succ
list
/list-as-arrayinstance/
len-05
nat-basic
/
one-01
list-del
/list-as-arrayinstance/
get-append-grt
array-copy
/
subarray-at
nat
/
les
nat
/
eqle-one
nat-basic
/
lf-01
nat
/
cancel-01
nat
/
zero
list-del
/list-as-arrayinstance/
one-03
nat
/
lez
nat-basic
/
zero
nat-basic
/
add-base
nat
/
lels-03