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Theorem heap-order-min
⊦ n ≠ 0 ∧ n ≤ # kar ∧ heap-order(kar, n) ∧ m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[0].key
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: 8
Proof steps: 25
Used lemmas:
heap-order
,
Used spec theorems:
Used simplifier rules:
nat
/
fle-01
key-index
/
elim
nat-div
/
two-zero-01-01
nat
/
lels-03
nat
/
elim-pred-c
nat
/
succ-01
oelem
/binheap-key/
nnn
oelem
/binheap-key/
nll
nat-div
/
two-ls-02
nat
/
fle
nat
/
lels
key-index
/
inj
nat-basic
/
one
nat-basic
/
f
nat-basic
/
zero
nat-basic
/
twols-02
nat-basic
/
one-01
nat-basic
/
succ
nat-basic
/
trans
nat-basic
/
lf
nat-basic
/
s-04
nat-basic
/
a
nat-basic
/
c
nat-basic
/
oz
nat
/
add-01
nat-basic
/
add-base
key-index
/
sel-02
nat-basic
/
nls-fst