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Theorem push-corr
inv(buf), abs(buf, x), buf .len < buf .size ⊦ 〈push#(a; buf)〉 (inv(buf) ∧ abs(buf, push(x, a)))
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: 30
Proof steps: 70
Used lemmas:
tolist-at
,
tolist-rec-inv
,
tolist-size
,
abs
,
Used spec theorems:
intnat
/
i2n-mod
intnat
/
add-01
int-basic2
/
add-c
list-del
/queue/
extension
array
/
cngetput
intnat
/
num-i2n-le
intnat
/
num-i2n-le-02
nat-div
/
mod-rec
nat
/
pls
intnat
/
num-n2i-ls-02
intnat
/
num-i2n-ls-02
nat-div
/
mod-eq
ring-buffer-inv
/
inv
Used simplifier rules:
int-abs
/
forward-le-04
int-abs
/
lep-01
int-div
/
mod-zero-04
int-div
/
div-elim
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lele
int-abs
/
lels
int-abs
/
succ-01
int-abs
/
numleledel-01
int-abs
/
numle-02
array
/
Size-put
nat-basic1
/
ls-02
nat-basic2
/
l
int-abs
/
lels-03
nat
/
anti
nat
/
ler
int-abs
/
forward-lsle
int-abs
/
absle
nat
/
fle-01
nat
/
lels-03
nat-basic2
/
eqs
intnat
/
labs
int-abs
/
abs-16
int-basic1
/
irref
nat
/
fle
nat-basic1
/
lf
nat-basic1
/
trans-1
nat-basic2
/
succ
nat-basic2
/
l-02
nat-basic2
/
l-01
nat-basic1
/
lf-01
nat-basic2
/
eq-01
nat-div
/
mod-eq
nat
/
lels-01
int-abs
/
anti
int-abs
/
lenls
int-basic1
/
ls-01
nat-mult
/
numeral-26
nat-mult
/
two-02
nat-basic1
/
lf-02
nat-mult
/
two-zero-01
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-mult
/
numeral-36
nat-mult
/
one
nat
/
le-ls-simp
nat
/
lep
nat
/
elim-sub
nat-basic1
/
one
int-basic1
/
forward-pos
int-abs
/
lels-02
intnat
/
abs-zero
nat-basic1
/
f
nat
/
lels
nat
/
ls-le-simp
intnat
/
abs-eq
list
/queue/
app-03
array
/
cgetput
nat-div
/
mod-ls
int-abs
/
lels-01
int-abs
/
zero-gs
int-div
/
mod-less-01
intnat
/
nat2int
intnat
/
n2n
int-abs
/
zero-gels-04
ring-buffer
/
sel-01
ring-buffer
/
sel-02
intnat
/
nat2int-02
ring-buffer
/
sel-04
ring-buffer
/
sel-03
ring-buffer
/
upd-04
ring-buffer
/
upd-01
ring-buffer
/
elim
ring-buffer
/
updsel-05
ring-buffer
/
updsel-08
ring-buffer
/
updsel-09
ring-buffer
/
updsel-12
ring-buffer
/
updsel-01
ring-buffer
/
updsel-04
intnat
/
rax-04
int-basic2
/
add-a
int-basic2
/
add-in
nat-basic2
/
c
nat-basic2
/
a
intnat
/
i2i-pos-01
intnat
/
n2i-add
list
/queue/
a
list
/queue/
len-02
list
/queue/
len
ring-buffer
/
updsel-16
int-basic2
/
add-c
nat-basic1
/
zero
intnat
/
num-n2i-ls-02
int-abs
/
forward-le-05
ring-buffer
/
updsel-13
int-abs
/
forward-le-01
int-abs
/
forward-lels
list
/queue/
Last
int-abs
/
abs-18
intnat
/
ini2-abs