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Theorem Inv-last-inner-init-b
i + 1 < # A, j ≠ 0, A[j - 1] ≤ x ⊦ Inv-first-inner(A, A0, x, y, i, j) → Inv-last-inner(A[j + 1, x], A0, x, y, i, j)
Type: A user defined theorem
Validity: The proof is valid.
Features: ss,
Comment:
Used by:
Used by units in proved state:
pair-insertion-sort
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 7
Used lemmas:
Inv-last-inner
,
Inv-first-inner
,
Used spec theorems:
oarray-sorted
/
sorted-inc-left
array
/
cputput-reverse
Used simplifier rules:
array
/
cgetput
nat
/
ls-add-not-01
nat
/
lels
nat
/
lep
nat
/
let
oarray-sorted
/
sorted-write-other
nat-basic
/
l-02
nat
/
elim-pred-c
oarray-sorted
/
sorted-mixup
nat
/
ge
nat
/
fle
oarray-sorted
/
sorted-merge
nat-basic
/
zero
nat
/
gr-def
array
/
cngetput
nat-basic
/
eq-02
nat-basic
/
oz
oarray-sorted
/
less-eq-elem
nat
/
lep-02
nat
/
le-def
nat-basic
/
ref
oarray-sorted
/
sorted-higher-lower-bound
oelem
/
transitivity
oelem
/
nll
oelem
/
irreflexivity
nat
/
cancel-01
nat-basic
/
one-01
oelem
/
ls-le
nat
/
eqle-one
nat-basic
/
f
nat-basic
/
lf-02
nat-basic
/
lf
nat-basic
/
trans
nat-basic
/
lf-01
nat
/
fle-01
nat
/
add-num-03
nat
/
ler
nat-basic
/
succ
nat-basic
/
l
nat-basic
/
l-01
nat-basic
/
s-04
nat
/
l-num-01
nat
/
succ-01
array
/
Size-put
oarray-sorted
/
sorted-0-or-1
nat-basic
/
eq-01
nat-basic
/
a
nat-basic
/
c