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Theorem suffix-max-sum-reset
n < # ar ⊦ i + ar[n] < 0 ∧ maximum-suffix-sum(subarray(ar, 0, n), m, i) → maximum-suffix-sum(subarray(ar, 0, n + 1), n + 1, 0)
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
Used by units in proved state:
kadane
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 7
Used lemmas:
sum-succ
,
suffix-upper-bound-reduce
,
sum-zero
,
sum-subarray
,
maximum-suffix-sum
,
Used spec theorems:
Used simplifier rules:
nat
/
le-one
int-abs
/
le-def
nat
/
zero
nat
/
cancel-01
nat
/
ler
nat
/
lep-02
nat
/
le
nat
/
le-ls-simp
array-copy
/int-array/
size-subarray
int-abs
/
forward-le-05
int-basic1
/
lf-01
int-basic1
/
trans
int-abs
/
forward-le-02
nat-basic
/
lf-02
nat
/
fle-01
nat-basic
/
eq-01
nat-basic
/
a
nat-basic
/
c
int-basic2
/
succ-01
int-basic2
/
add-a
int-basic2
/
add-c
int-basic2
/
lst-03
int-abs
/
zero-gels-01
nat
/
lels-03
nat
/
lep
nat
/
succ-01
int-basic2
/
ls-01
int-abs
/
lenls
array-copy
/int-array/
subarray-elim
nat
/
lels
nat
/
ls-le-simp
nat
/
le-def
nat
/
eqle-one
nat
/
fle
nat-basic
/
f
nat
/
le-add
nat-basic
/
add-base
int-abs
/
numls-03
nat
/
elim-sub