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Theorem prepost-insert
bin-heap-inv(bh, ar), ar0 = ar, bh0 = bh, ki.idx < # ar, ∀ ki0. ki0 ∈ keyset(bh0) → ki0.idx ≠ ki.idx ⊦ ⟪bin_min_heap_insert#(ki; bh, ar)⟫ (bin-heap-inv(bh, ar) ∧ id-idx(ar0, ar) ∧ keyset(bh) = keyset(bh0) ++ ki)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 56
Used lemmas:
bubble-up-inv
,
prepost-bubble-up
,
prepost-resize
,
keyset
,
bin-heap-inv-def
,
Used spec theorems:
bin-min-heap-inv
/
valid-idx-rec
bin-min-heap-inv
/
heap-order-add-smaller
bin-min-heap-inv
/
keyset-subarray-eq
Used simplifier rules:
bin-min-heap
/
elim
bin-min-heap
/
inj
key-index
/
elim
nat
/
lels-03
nat
/
ge
bin-min-heap
/
upd-02
bin-min-heap
/
upd-01
nat-basic
/
lf-02
bin-min-heap-inv
/
no-dups-idx-rec
set-basic
/keyindex-set/
ne
set-basic
/keyindex-set/
size-zero
key-index
/
sel-01
set-basic
/keyindex-set/
size-zero-01
set-basic
/keyindex-set/
ne-01
bin-min-heap-inv
/
heap-order-1
nat-basic
/
zero
bin-min-heap-inv
/
heap-order-0
bin-min-heap-inv
/
no-dups-idx-0
bin-min-heap-inv
/
valid-idx-0
nat
/
lez
oelem
/binheap-key/
nll
oelem
/binheap-key/
transitivity
oelem
/binheap-key/
irreflexivity
nat
/
le-def
nat-basic
/
lf
nat-basic
/
trans
nat
/
add-num-03
nat-basic
/
succ
nat-basic
/
l
nat-basic
/
succ-03
bin-min-heap-inv
/
key-set-write-last
array
/key-index-array/
cputput
nat
/
ls-le-simp
nat
/
lels
key-index
/
sel-02
array
/key-index-array/
Put-same
index-array
/
id-idx-refl
index-array
/
id-idx-write
index-array
/
id-idx-write-left
array
/key-index-array/
Size-put
bin-min-heap
/
sel-02
nat-basic
/
ref
nat-basic
/
s-04
nat-basic
/
add-base
nat
/
add-01
bin-min-heap
/
sel-01
nat
/
eqle-one
array-copy
/key-index-array/
subarray-zero
bin-min-heap-inv
/
keyset-base
nat
/
elim-pred-c
nat-basic
/
f
set-basic
/keyindex-set/
In-insert
nat-basic
/
oz
array
/key-index-array/
cngetput
nat-div
/
two-neq-01
nat-basic
/
lf-01
bin-min-heap-inv
/
keyset-rec
nat-basic
/
a
nat-basic
/
c
array-copy
/key-index-array/
subarray-elim
nat
/
succ-01
nat-basic
/
nls-fst