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Theorem subarray-split-first
⊦ n1 ≠ 0 ∧ n0 + n1 ≤ # ar → subarray(ar, n0, n1) = mkarray(1)[0, ar[n0]] + subarray(ar, n0 + 1, n1 - 1)
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: 4
Proof steps: 13
Used lemmas:
append-at2
,
append-at1
,
append-a
,
append-len
,
Used spec theorems:
array
/
Extension
array-copy
/
subarray-at
Used simplifier rules:
nat
/
lels
nat-basic
/
eq-01
nat-basic
/
add-base
array
/
cgetput
nat
/
le-def
nat-basic
/
one-01
nat
/
let
nat
/
not-zero
nat
/
le-ls-simp
nat-basic
/
s-04
array-copy
/
size-subarray
array
/
Size-mkarray
array
/
Size-put
nat-basic
/
oz
nat-basic
/
a
nat-basic
/
c
nat
/
lep
nat
/
succ-01
nat-basic
/
f
array-copy
/
subarray-at
nat
/
elim-pred-c