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Theorem sorted-next-1-swap
n + 1 < # x ⊦ partial-sorted(x, 1, n) ∧ x[n + 1] < x[n] ∧ n % 2 = 1 → partial-sorted(x[n, x[n + 1]][n + 1, x[n]], 1, n + 2)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
odd-even-sort
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 15
Used lemmas:
partial-sorted
,
Used spec theorems:
list-del
/
put-length
list-del
/
put-at-eq
list-del
/
put-at
Used simplifier rules:
nat-basic
/
l
nat-mult
/
modls
nat
/
l-num-02
list-del
/
put-at-eq
nat
/
ls-le-simp
nat-basic
/
ref
nat-mult
/
two-ls-01
nat-basic
/
s-04
nat
/
lep-02
nat-div
/
two-odd
nat
/
eqle-one
oelem
/
transitivity
oelem
/
irreflexivity
list-data
/
l
nat-basic
/
f
nat-basic
/
succ-03
nat
/
add-num-01
nat-div
/
mod-mult-01
list-del
/
put-at
nat-basic
/
l-02
nat
/
fle
nat
/
lels
nat-basic
/
eq-01
nat-basic
/
nls-fst
nat-basic
/
l-06
nat-basic
/
lf-02
nat-basic
/
lf-01
nat-div
/
mod-mult
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-basic
/
succ
nat-basic
/
trans
nat-basic
/
lf
list-del
/
put-length
nat-basic
/
neq-01
nat-basic
/
between
nat-basic
/
a
nat-basic
/
c