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Theorem valid-idx-move-last
⊦ m < # kar ∧ valid-idx(kar, ar, m + 1) ∧ kar[m] = key-index(key, m1) → valid-idx(kar[m0, key-index(key, m1)], ar[m1, ar[m1].idx:= m0], m)
Type: A user defined theorem
Validity: The proof is valid.
Features: s,
Comment:
Used by:
Used by units in proved state:
bin-min-heap-prepost
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 31
Used lemmas:
valid-idx
,
Used spec theorems:
Used simplifier rules:
nat-basic
/
s-04
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
array
/index-array-base/
Size-put
nat
/
lels-03
array
/key-index-array/
Size-put
key-index
/
elim
array
/index-array-base/
Put-same
elem-index
/
elim
array
/key-index-array/
Put-other
elem-index
/
inj
elem-index
/
upd-02
nat-basic
/
succ
nat
/
le-ls-simp
nat
/
lels
nat-basic
/
ref
nat
/
fle
nat-basic
/
lf-01
array
/index-array-base/
Put-other
array
/key-index-array/
Put-same
key-index
/
inj
nat-basic
/
ls-02
nat-basic
/
lf-02
key-index
/
sel-01
nat-basic
/
f
nat-basic
/
lf
nat-basic
/
trans
elem-index
/
sel-02