[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem heap-order-overwrite-children-ok
n ≤ # kar, m < n ⊦ heap-order(kar, n) ∧ ¬ ki.key < kar[m].key ∧ (2 * m + 1 < n → ¬ kar[2 * m + 1].key < ki.key) ∧ (2 * m + 2 < n → ¬ kar[2 * m + 2].key < ki.key) → (¬ 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: 5
Proof steps: 21
Used lemmas:
heap-order
,
Used spec theorems:
array
/key-index-array/
Put-other
Used simplifier rules:
nat
/
elim-pred-c
key-index
/
elim
array
/key-index-array/
cngetput
nat-div
/
div-elim
nat-basic
/
nls-fst
nat-basic
/
f
nat-basic
/
succ
nat
/
l-num-05
nat-basic
/
one-01
nat
/
fle
oelem
/binheap-key/
nnn
key-index
/
sel-02
nat-basic
/
add-base
nat
/
add-01
nat-basic
/
oz
key-index
/
inj
nat-mult
/
rsucc-02
nat-basic
/
a
nat-basic
/
c
nat-mult
/
mult-a
nat-mult
/
mult-c
array
/key-index-array/
Put-same
nat-div
/
two-neq-01
oelem
/binheap-key/
lel
oelem
/binheap-key/
nll
oelem
/binheap-key/
nen