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Theorem sum-all-indices-le
∀ n. 0 ≤ n ∧ n < # ints → ints[n] ≤ ints0[n], # ints = # ints0 ⊦ Σ ints ≤ Σ ints0
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: 11
Used lemmas:
sum-rec-01
,
sum-rec
,
sum-empty
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-02
nat
/
lez
list-data
/intlista/
size-01
nat-basic2
/
oz
list-data
/intlista/
elim-list-c
list
/intlista/
e-01
nat-basic2
/
eq-01
list
/intlista/
len-02
list
/intlista/
len
list
/intlista/
c
list-del
/intlista/
get-zero-01
nat-basic1
/
zero-01
list-data
/intlista/
l
nat-basic1
/
f
nat-basic1
/
lf-01
int-abs
/
lels-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
int-simp-07
nat-basic2
/
s
nat-basic2
/
a
nat-basic2
/
c
list-del
/intlista/
get-succ
list
/intlista/
a
int-abs
/
lels-03