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Theorem payload-shift-left
⊦ n ≤ nused ∧ nused < # zbrar ∧ sorted(zbrar, 0, nused + 1) → payload(shl(zbrar, n, nused + 1), 0, nused) = (zbrar[n].entry? ⊃ payload(zbrar, 0, nused + 1) -- zbrar[n].key;payload(zbrar, 0, nused + 1))
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 36
Proof steps: 118
Used lemmas:
at-payload
,
in-payload
,
Used spec theorems:
store
/node-index/
k-Extension
Used simplifier rules:
store
/node-index/
Del-at-strong
store
/node-index/
Del-in
zbranch
/
elim-03
nat
/
let
nat-basic
/
l-08
nat-basic
/
eq-01
nat-basic
/
l-05
nat
/
ls-le-simp
nat
/
le
nat
/
add-01
znode-ops
/
at-shl
nat-basic
/
l-02
znode-ops
/
size-shl
nat-basic
/
add-base
nat-basic
/
ls-02
nat-basic
/
l
zbranch-array-sorted
/
sorted-eq-entry-strong
nat
/
eq
nat
/
fle-01
nat
/
le-one
zbranch
/
inj-01
nat
/
lez-01
nat-basic
/
zero
nat
/
les
nat
/
eqle-one
nat-basic
/
lf-02
nat-basic
/
lf-01
nat
/
lep-02
oelem
/nat-set/
irreflexivity
oelem
/nat-set/
ls-le
nat
/
anti
nat
/
ler
nat
/
fle
nat
/
lels-03
nat
/
le-ls-simp
nat
/
ls-01
nat-basic
/
f
nat-basic
/
one-01
nat
/
le-def
nat-basic
/
oz
nat-basic
/
a
nat-basic
/
c
nat
/
succ-01
nat-basic
/
s-04
nat
/
lels
nat-basic
/
lf
oelem
/nat-set/
transitivity
nat-basic
/
succ
zbranch
/
test-05
zbranch
/
sel-04
nat
/
lez
nat-basic
/
zero-01
nat
/
elim-pred-c