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Theorem permut-correct
ar0 = ar ⊦ ⟨permut#(; ar, listofar)⟩ (¬ dups(listofar) ∧ ordered≤(listofar) ∧ listofar.toSet = allPerms(ar0))
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: 22
Proof steps: 51
Used lemmas:
perm-all-perms-eq
,
max-smaller-perms-all-perms
,
greater-perms
,
next-perm-greaterPerms
,
next-perm-smallerPerms
,
next-permutation
,
smaller-perms
,
toSet
,
ordered-append
,
next-proper-permutation
,
ordered-smallerPerms
,
nil-toSet
,
ordered-arraylist-base0
,
sort-def
,
permut
,
Used spec theorems:
set-basic
/array-set/
Extension
list-perm
/natarray-oarray-sort/
trans
list-perm
/natarray-oarray-sort/
sym
set-basic
/array-set/
Size-insert
Used simplifier rules:
list
/list-of-natarray/
Last
list-dup
/list-of-natarray/
e-01
list-perm
/natarray-oarray-sort/
ref
list
/list-of-natarray/
a
list
/list-of-natarray/
in-17
list
/list-of-natarray/
in-append
list
/list-of-natarray/
in-15
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
list-dup
/list-of-natarray/
f
list-perm
/natarray-oarray-sort/
neq
set-basic
/array-set/
In-insert
nat-basic
/
f
nat-basic
/
add-base
oelem
/natarray/
irreflexivity
nat
/
lels
nat
/
succ-01
set-basic
/array-set/
eq
nat
/
ler