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Theorem heap-order-pull-up-child
n ≤ # kar, m < n ⊦ heap-order(kar, n) ∧ 2 * m + 1 < n ∧ ki = (2 * m + 2 < n ∧ kar[2 * m + 2].key < kar[2 * m + 1].key ⊃ kar[2 * m + 2];kar[2 * m + 1]) → (¬ heap-order(kar[m, ki], n) ↔ false)
Type: A user defined theorem
Validity: The proof is valid.
Features:
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: 3
Proof steps: 31
Used lemmas:
heap-order
,
Used spec theorems:
nat-div
/
div-two-mult
Used simplifier rules:
key-index
/
elim
nat-basic
/
add-base
array
/key-index-array/
cngetput
oelem
/binheap-key/
transitivity
nat-div
/
two-odd-01
nat-div
/
mult-02
nat-div
/
two-ls-04
nat-mult
/
two-zero-01
nat-basic
/
f
oelem
/binheap-key/
irreflexivity
nat-basic
/
l
nat-div
/
mod-eq-02
nat-basic
/
oz
nat
/
elim-pred-c
oelem
/binheap-key/
nen
array
/key-index-array/
Put-other
nat-div
/
two-neq-01
array
/key-index-array/
Put-same
nat-mult
/
rsucc-02
oelem
/binheap-key/
lel
key-index
/
inj
nat
/
add-num-03
nat-basic
/
a
nat-basic
/
c
nat
/
add-01
nat-div
/
two-two-01
nat-mult
/
mult-a
nat-mult
/
mult-c
key-index
/
sel-02
nat
/
fle
oelem
/binheap-key/
nnn
oelem
/binheap-key/
nll
nat
/
lels