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Theorem multi-in-other
⊦ ¬ r ∈ refs ∧ # refs = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- sk ∈ addmultiarrays(refs, i, acc, ty, ints, st) ↔ r -- sk ∈ st)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
addarrays-refin
,
multi-isarrayref-01
,
multi-isarrayref-notin
,
multi-refin-other
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 35
Used lemmas:
countrefs-one
,
countrefs-zero
,
countrefs-lastn-03
,
countrefs-lastn
,
countrefs-rec-02
,
countrefs-inrefs
,
countrefs-not-zero-01
,
countrefs-i2n
,
countrefs-rec-01
,
addmultiarrays-rec
,
addmultiarrays-done
,
addmultiarrays-base
,
Used spec theorems:
list-del
/references/
lastn-neq-04
list-del
/references/
lastn-neq
Used simplifier rules:
addarray
/
in-1dim-03
addarray
/
in-1dim-01
list
/intlista/
in-empty
list-last
/intlista/
b
valuesfuns
/
posints-empty
list
/intlista/
app
addarray
/
in-1dim-14
list-data
/references/
l
addarray
/
in-init-01
addarray
/
in-1init
storefuns
/
instore-01
addarray
/
in-init-09
int-basic2
/
ax-04
int-abs
/
numsub
intnat
/
n2i-add
nat
/
le-ls-simp
nat
/
lep-02
oelem
/intlista/
irreflexivity
list
/intlista/
c-08
list
/intlista/
in-01
list-last
/intlista/
bin
valuesfuns
/
posints-rec-01
int-abs
/
lels-04
int-abs
/
lels-01
list
/intlista/
e
list
/intlista/
app-02-ant
list
/references/
in-01
nat
/
lep
nat-mult
/
coef-18
nat
/
lep-01
nat
/
lels
nat-basic2
/
l
list-del
/references/
first-length
list
/references/
in-06
list
/references/
e-01
nat-basic2
/
eq-01
list
/references/
len-02
list
/references/
len
list-data
/references/
size-01
list-del
/references/
firstN-rec
nat-basic2
/
eqs
nat
/
lels-01
nat-basic1
/
lf-02
nat-basic1
/
f
nat-basic2
/
l-02
nat
/
elim-sub
list
/references/
in-17
list
/references/
in-append
list
/references/
a
list
/references/
in-14
list-del
/references/
lastN-empty
intnat
/
abs-zero
list-data
/references/
elim-list-c
int-mult
/
commutativity
int-mult
/
associativity
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
rsucc-02
intnat
/
rax-04
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
succ-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numadd-01
int-abs
/
elim-sub
list
/references/
c
list
/intlista/
c-07
int-abs
/
ax-02
int-abs
/
lels
int-basic1
/
ls-01
nat-basic2
/
one-03
nat-basic2
/
oz
nat-basic1
/
one
nat
/
ax-02
int-abs
/
forward-le-05
int-abs
/
lels-02
list
/intlista/
in-06
list-last
/intlista/
bapp
nat-basic2
/
c
nat-basic2
/
a
list-data
/intlista/
l
nat-basic2
/
one
list
/intlista/
len-02
list
/intlista/
len
int-abs
/
zero-gels-04
valuesfuns
/
posints-rec
list
/intlista/
a
list
/intlista/
e-01
list
/intlista/
c
list-data
/intlista/
elim-list-c
int-abs
/
forward-le-01