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Theorem heap-order-add-parent-key
n + 1 ≤ # kar, n ≠ 0 ⊦ heap-order(kar, n) ∧ kar[(n - 1) / 2] = key-index(key, m) → heap-order(kar[n, key-index(key, m)], n + 1)
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 17
Used lemmas:
heap-order
,
Used spec theorems:
array
/key-index-array/
Put-other
Used simplifier rules:
nat
/
fle-01
nat
/
lels
nat
/
succ-01
nat
/
elim-pred-c
nat-basic
/
s-04
nat
/
lep-02
key-index
/
elim
nat-div
/
two-neq-01
array
/key-index-array/
cngetput
nat
/
ler
oelem
/binheap-key/
lel
oelem
/binheap-key/
irreflexivity
nat
/
lels-02
nat-basic
/
eq-01
key-index
/
inj
array
/key-index-array/
Put-same
nat-basic
/
f
nat-basic
/
lf-02
nat-mult
/
rsucc-02
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-mult
/
numeral-28
nat-mult
/
one
nat
/
add-num-03
nat-mult
/
ls-08
nat-div
/
div-elim
nat-basic
/
neq-04
nat-basic
/
ls-02
nat-basic
/
a
nat-basic
/
c
nat-basic
/
oz
nat
/
add-01
nat-basic
/
add-base
key-index
/
sel-02