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Theorem Inv-last-inner-init-a
i + 1 < # A ⊦ j = 0 ∧ 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, cut,
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: 4
Proof steps: 7
Used lemmas:
Inv-last-inner
,
Inv-first-inner
,
Used spec theorems:
oarray-sorted
/
sorted-inc-left
oarray-sorted
/
sorted-0-or-1
array
/
cputput-reverse
Used simplifier rules:
array
/
cgetput
nat-basic
/
nls-fst
nat-basic
/
lf-01
oarray-sorted
/
sorted-write-other
oarray-sorted
/
sorted-emtpy
nat
/
lez
nat-basic
/
twols
nat-basic
/
succ
nat
/
fle-01
nat-basic
/
trans
nat-basic
/
lf
nat-basic
/
lf-02
oelem
/
ls-le
nat-basic
/
f
oelem
/
irreflexivity
oelem
/
nll
oelem
/
transitivity
oarray-sorted
/
sorted-higher-lower-bound
oarray-sorted
/
less-eq-elem
nat-basic
/
c
nat-basic
/
a
array
/
Size-put
nat
/
lels-02
nat-basic
/
one
nat
/
le-def
nat-basic
/
one-01
nat-basic
/
twols-02
oarray-sorted
/
sorted-0-or-1