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Theorem sorted-insert-merge
0 < m ⊦ sorted(A, 0, m) ∧ sorted(A, m + 1, n) ∧ A[m - 1] ≤ a ∧ a ≤ A[m + 1] → sorted(A[m, a], 0, n)
Type: A user defined theorem
Validity: The proof is valid.
Features:
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: 10
Used lemmas:
sorted
,
less-eq-elem
,
Used spec theorems:
array
/
Put-other
Used simplifier rules:
array
/
Size-put
nat-basic
/
zero
nat
/
lez
nat
/
elim-pred-c
oelem
/
nnn
nat
/
succ-01
nat-basic
/
oz
array
/
cngetput
nat-basic
/
lf-02
array
/
Put-same
nat-basic
/
eq-01
nat-basic
/
eq-02
nat
/
lels
nat
/
les
nat
/
eqle-one
nat-basic
/
lf-01
nat
/
fle
nat
/
ler
nat-basic
/
l
array
/
cgetput
nat-basic
/
succ-03
nat-basic
/
c
nat-basic
/
a
nat-basic
/
f
nat-basic
/
neq-01