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Theorem sum-all-elems-le
∀ i. i ∈ ints → i ≤ i0 ⊦ Σ ints ≤ i0 * n→i(# ints)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
int-fac
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 11
Used lemmas:
sum-rec
,
sum-empty
,
Used spec theorems:
int-mult
/
dist-lsplit
Used simplifier rules:
list-data
/intlista/
size-01
int-mult
/
Mult-zero
list
/intlista/
in-17
list
/intlista/
in-append
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list
/intlista/
len-02
list
/intlista/
len
list
/intlista/
a
list
/intlista/
c
int-abs
/
lels-01
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
forward-lels
int-mult
/
one
int-mult
/
associativity
int-basic2
/
ls-01
int-abs
/
lenls
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
commutativity