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Theorem fill2append
⊦ n0 + n1 ≤ # ar → fill(ar, a, n0, n1) = subarray(ar, 0, n0) + fill(mkarray(n1), a) + subarray(ar, n0 + n1, # ar - n0 + n1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 17
Used lemmas:
append-at2
,
append-at1
,
append-a
,
append-len
,
Used spec theorems:
array
/
Extension
array-copy
/
at-fill-h
Used simplifier rules:
array-copy
/
size-fill-h
nat
/
ls-le-simp
nat-basic
/
add-base
nat
/
fle
nat
/
let
nat-basic
/
ref
array-copy
/
subarray-elim
nat-basic
/
l-06
nat-basic
/
lf-01
array-copy
/
at-fill-mkarray
nat-basic
/
l-01
nat
/
fle-01
nat
/
le-ls-simp
nat
/
lels
array-copy
/
size-subarray
array
/
Size-mkarray
array-copy
/
size-fill
nat
/
lep
nat-basic
/
a
nat-basic
/
c
nat-basic
/
l
nat-basic
/
f
array-copy
/
subarray-at
nat
/
elim-sub