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Theorem array-le-same-prepart
⊦ ar1 ≤ ar2 ∧ ar2 ≤ ar3 ∧ subarray(ar1, 0, m) = subarray(ar3, 0, m) ∧ m < # ar1 ∧ m < # ar2 ∧ m < # ar3 → subarray(ar1, 0, m) = subarray(ar2, 0, m)
Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by:
array-le-same-prepart2
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 13
Used lemmas:
array-le-same-prefix
,
array-le-trans
,
array-split-into-subarrays
,
Used spec theorems:
array
/natarray/
Extension
list-del
/natarray-oarray-sort/
get-append-less
Used simplifier rules:
list-data
/natarray-oarray-sort/
l
nat-basic
/
f
nat
/
lels-03
nat
/
elim-sub
nat-basic
/
c
nat-basic
/
a
nat-basic
/
l-01
nat-basic
/
lf-01
list
/natarray-oarray-sort/
a
array-copy
/natarray/
size-subarray
list
/natarray-oarray-sort/
len
nat-basic
/
add-base
array-copy
/natarray/
subarray-at
list-del
/natarray-oarray-sort/
get-append-grt
nat
/
lels
nat
/
ls-le-simp