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Theorem allslotsfull-inc
n1 < # ar, n0 < # ar ⊦ n = (n1 + 1) % # ar ∧ ar[n1] ≠ e ∧ ar[n1] ≠ ⊥ → (allslotsfull(ar, n0, n1, e, false) ↔ allslotsfull(ar, n0, n, e, true))
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 24
Used lemmas:
between-def
,
allslotsfull-def
,
Used spec theorems:
nat-div
/
rax
nat-div
/
rec
Used simplifier rules:
nat-basic
/
f
nat-div
/
mod-ls
nat-div
/
cond
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
nat
/
ls-03
nat
/
lez
nat-basic
/
one-01
nat-basic
/
l
nat
/
ls
nat
/
lels
nat
/
let
nat
/
fle-01
nat
/
anti
nat-basic
/
add-base
nat-basic
/
lf-02
nat
/
ler
nat-mult
/
ls-08
nat-mult
/
zero-06
nat-mult
/
zero-01
nat
/
les
nat-mult
/
rsucc-02
nat
/
eqle-one
nat-basic
/
lf-01
nat-basic
/
refl-Nat
nat
/
cancel-01
nat
/
zero
nat-basic
/
oz
nat-div
/
zero
nat-mult
/
zero
nat-basic
/
l-02
nat-basic
/
ls-02
nat
/
fle
nat
/
le-ls-simp
nat-basic
/
s-04
nat-mult
/
ls-10
nat-mult
/
two-02
nat-mult
/
le-02
nat
/
lep-02
nat-basic
/
succ-03
nat-div
/
zero-01
nat-basic
/
succ
nat-basic
/
trans-Nat
nat-basic
/
lf
nat-div
/
modsucc-less
nat-basic
/
zero
nat-div
/
mod-zero
nat-basic
/
one
nat-basic
/
one-04
nat
/
le-sum
nat
/
ls-le-simp
nat-div
/
mod-eq
nat-basic
/
l-06
nat
/
lels-03
nat-basic
/
neq-01
nat
/
le-def