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Theorem range-eq-splice-less
⊦ m1 ≤ m0 ∧ n + m0 ≤ # ar ∧ # ar0 < n0 + m1 ∧ m1 ≠ 0 ∧ n1 ≤ n0 → (range=(ar2, n2, splice(ar, n, ar0, n0, m0), n1, m1) ↔ range=(ar2, n2, splice(ar, n, ar0, n0, m1), n1, m1))
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 24
Proof steps: 47
Used lemmas:
resize-at
,
splice-0
,
splice-len
,
resize-len
,
range-eq-ext
,
splice-resize
,
Used spec theorems:
min-max
/
max
nat
/
le-addex
array-copy
/
at-copy
Used simplifier rules:
min-max
/
max-second-le
min-max
/
max-first-ls
nat-basic
/
l-02
nat
/
cancel-01
nat-basic
/
l-04
nat
/
ls-le-simp
nat
/
lep-02
array-copy
/
size-copy
nat-basic
/
add-base
nat
/
lez-01
nat
/
fle
nat
/
le-sum
nat
/
lels
nat
/
fle-01
nat-basic
/
l
nat
/
le-ls-simp
nat-basic
/
a
nat-basic
/
c
nat-basic
/
f