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Theorem splice-resize-less
⊦ n1 ≤ m1 ∧ m0 ≠ 0 → resize(splice(ar0, n0, ar1, n1, m0), m1) = resize(splice(ar0, n0, ar1, n1, min(m0, m1 - n1)), m1)
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: 21
Proof steps: 47
Used lemmas:
splice-copy
,
splice-resize
,
splice-0
,
splice-len
,
resize-at
,
resize-len
,
Used spec theorems:
min-max
/
min
array
/
Extension
min-max
/
max
array-copy
/
at-copy
Used simplifier rules:
nat
/
elim-sub
nat-basic
/
eq-01
nat-basic
/
add-base
nat
/
lez
min-max
/
max-notls2
nat
/
lels-03
min-max
/
max-notls1
nat
/
fle
nat
/
lep
min-max
/
max-second-le
array-copy
/
at-copy
nat-basic
/
lf
nat-basic
/
trans
nat-basic
/
succ
nat
/
le-ls-simp
nat-basic
/
f
min-max
/
max-first-ls
nat
/
le-def
nat-basic
/
l-01
nat
/
fle-01
nat
/
add-01
nat-basic
/
l-02
nat-basic
/
a
nat-basic
/
c
nat
/
lep-02
nat
/
ls-le-simp
nat
/
eq-01
nat-basic
/
l
nat
/
lels