[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem Inv-first-inner-init-b
y ≤ x, x = A[i + 1], y = A[i] ⊦ i + 1 < # A ∧ Inv-main(A, A0, i) → Inv-first-inner(A, A, x, y, i, i)
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: 0
Proof steps: 2
Used lemmas:
Inv-first-inner
,
Inv-main
,
Used spec theorems:
Used simplifier rules:
oarray-perm
/
perm-ident
nat
/
ls-le-simp
array
/
putgetinv
nat-basic
/
l-02
nat
/
anti
nat
/
lels
oarray-sorted
/
sorted-0-or-1
nat-basic
/
ref
nat-basic
/
l
nat-basic
/
succ
nat-basic
/
l-01
nat
/
add-num-03
oarray-perm
/
perm-trans
nat-basic
/
trans
nat-basic
/
lf
nat
/
fle-01
nat-basic
/
lf-02
nat-basic
/
one-01
nat
/
le-def
nat-basic
/
c
nat-basic
/
a
nat
/
zero
nat
/
cancel-01
nat-basic
/
lf-01
oarray-sorted
/
sorted-higher-lower-bound
nat
/
ler
nat-basic
/
f
oarray-sorted
/
less-eq-elem