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Theorem product-all-elems-le
∀ i. i ∈ ints → 0 < i ∧ i ≤ i0 ⊦ Π 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:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 19
Used lemmas:
Used spec theorems:
int-pot
/
Pot-pos
int-mult
/
commutativity
int-mult
/
pnls-pos
intlist
/
product-negative
Used simplifier rules:
list-data
/intlista/
size-01
int-pot
/
Pot-zero
intlist
/
prod-empty
list
/intlista/
in-17
list
/intlista/
in-append
intlist
/
prod-rec
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list
/intlista/
a
list
/intlista/
len-02
list
/intlista/
len
list
/intlista/
c
int-basic2
/
pred
int-basic2
/
add-c
int-basic2
/
add-a
intnat
/
nat2int
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
forward-le-05
int-abs
/
forward-le
int-abs
/
forward-lele
int-abs
/
forward-le-01
int-abs
/
zero-gels-04
int-abs
/
lels-03
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
oelem
/intlista/
transitivity
int-abs
/
lels-01
int-basic1
/
ls-01