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Theorem prepost-create-gcheap
lpt0 = lpt ⊦ ⟪persistence_create_gcheap#(nx; lpt, gch)⟫ (bin-heap-inv(gch, lpt) ∧ gc-heap(lpt, nx) = keyset(gch) ∧ id-idx(lpt0, lpt))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
inv-recover
,
Used by units in proved state:
persistence-refine
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 50
Used lemmas:
nat-stuff0
,
create-gcheap
,
Used spec theorems:
bin-min-heap-prepost
/gc-heap-rename-gc-heap-base/
bin-heap-inv-def
bin-min-heap-prepost
/gc-heap-rename-gc-heap-base/
prepost-insert
persistence-base
/
gc-heap-in-h
persistence-base
/
gc-heap-rec
persistence-base
/
gc-heap
index-array
/gc-heap-base/
id-idx
Used simplifier rules:
persistence-base
/
id-idx-gcheap
index-array
/gc-heap-base/
id-idx-refl
persistence-base
/
gc-heap-base
nat
/
lez
bin-min-heap
/gc-heap-base/
sel-01
bin-min-heap
/gc-heap-base/
sel-02
array
/gc-heap-base-key-index-array/
Size-mkarray
bin-min-heap-inv
/gc-heap-rename-gc-heap-base/
no-dups-idx-0
bin-min-heap-inv
/gc-heap-rename-gc-heap-base/
valid-idx-0
bin-min-heap-inv
/gc-heap-rename-gc-heap-base/
2exp-size-1
bin-min-heap-inv
/gc-heap-rename-gc-heap-base/
heap-order-0
nat
/
elim-sub
bin-min-heap-prepost
/gc-heap-rename-gc-heap-base/
keyset-eq-empty
key-index
/gc-heap-rename-gc-heap-base/
elim
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
size-zero-01
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
ne-01
bin-min-heap
/gc-heap-base/
elim
nat-basic
/
l-02
key-index
/gc-heap-rename-gc-heap-base/
sel-01
index-array
/gc-heap-base/
id-idx-trans
gc-heap-rename
/
id-idx-ls0
nat-basic
/
lf-02
nat
/
lep-02
nat-basic
/
l-01
elem-index
/gc-heap-base/
sel-01-M03
elem-index
/gc-heap-base/
sel-01-M02
elem-index
/gc-heap-base/
sel-01-M01
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unadd
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
une
oelem
/nat-set/
irreflexivity
nat-basic
/
s-04
nat
/
prop-07
nat
/
ls-01
nat
/
ls-le-simp
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
nat
/
lels-03
gc-heap-rename
/
id-idx-imp-ls-1
nat-basic
/
f
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
unc
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
una
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
uneq
set-union
/gc-heap-rename-gc-heap-base-keyindex-set/
One
gc-heap-rename
/
id-idx-fwd-0
set-basic
/gc-heap-rename-gc-heap-base-keyindex-set/
sub-e
lprops
/
elim
nat
/
ler
nat
/
anti
nat
/
lels
persistence-base
/
gc-heap-ididx-h
nat
/
le-ls-simp
nat
/
le-def