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Theorem keys-shift-left
⊦ n ≤ nused ∧ nused < # zbrar ∧ sorted(zbrar, 0, nused + 1) → keys(shl(zbrar, n, nused + 1), 0, nused) = keys(zbrar, 0, nused + 1) -- zbrar[n].key
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: 16
Proof steps: 33
Used lemmas:
in-keys
,
Used spec theorems:
set-basic
/node-index/
Extension
zbranch-array-sorted
/
sorted-all
Used simplifier rules:
set-union
/node-index/
Delete
nat
/
lep-02
nat
/
le
nat
/
add-01
znode-ops
/
at-shl
nat-basic
/
l-02
nat
/
le-def
znode-ops
/
size-shl
nat
/
ls-le-simp
nat-basic
/
add-base
nat
/
le-ls-simp
oelem
/key-order/
lel
oelem
/key-order/
irreflexivity
nat-basic
/
ls-02
nat-basic
/
s-04
nat
/
fle-01
nat
/
fle
nat
/
let
nat
/
lels
nat
/
lez-01
nat
/
elim-pred-c
nat
/
lels-03
nat
/
le-one
nat-basic
/
succ
oelem
/nat-set/
transitivity
nat-basic
/
lf
nat-basic
/
f
nat
/
succ-01
nat-basic
/
oz
nat
/
les
nat-basic
/
a
nat-basic
/
c