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Theorem prepost-resize
bin-heap-inv(bh, ar), bh0 = bh ⊦ ⟪bin_min_heap_resize#(minsize; bh)⟫ (bin-heap-inv(bh, ar) ∧ bh.size = bh0.size ∧ # bh.ar ≥ minsize ∧ subarray(bh.ar, 0, bh.size) = subarray(bh0.ar, 0, bh0.size))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
prepost-insert
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 19
Proof steps: 58
Used lemmas:
prepost-next2pot
,
bin-heap-inv-def
,
Used spec theorems:
bin-min-heap-inv
/
no-dups-idx
bin-min-heap-inv
/
valid-idx
array-copy
/key-index-array/
at-copy
nat
/
le-addex
bin-min-heap-inv
/
heap-order
Used simplifier rules:
nat
/
ge
bin-min-heap
/
elim
bin-min-heap
/
upd-01
array-copy
/key-index-array/
subarray-copy-elim-exact
key-index
/
elim
nat
/
lels-03
array-copy
/key-index-array/
size-copy
elem-index
/
elim
bin-min-heap-inv
/
valid-idx-last-valid
nat-basic
/
lf-02
key-index
/
sel-01
elem-index
/
sel-02
nat
/
elim-pred-c
nat-basic
/
succ
nat-basic
/
trans
nat
/
ls-le-simp
nat
/
l-num-06
array-copy
/key-index-array/
copy-exact
nat-basic
/
lf
nat
/
lels-02
nat-div
/
two-ls
nat-div
/
two-two-01
nat-mult
/
ls-08
array
/key-index-array/
Size-mkarray
nat
/
sub-base
nat-div
/
le-div-to-mult
nat-basic
/
zero-01
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-mult
/
two-zero-01
nat-basic
/
oz
nat-basic
/
a
nat-basic
/
c
nat
/
add-01
nat-basic
/
add-base
key-index
/
sel-02
bin-min-heap
/
sel-01
nat
/
gr-def
nat
/
lels
bin-min-heap
/
sel-02
nat
/
le-def
nat
/
fle
nat
/
let
nat
/
fle-01
nat-basic
/
f
nat
/
le-ls-simp