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Theorem datasize-append-empty-h
⊦ m ≤ # buf0 + # buf1 ∧ (m ≥ # buf0 → datasize(buf1, m - # buf0) = 0) → datasize(buf0 + buf1, m) = datasize(buf0, min(m, # buf0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
datasize-append-h-new
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 32
Used lemmas:
datasize-rec
,
datasize-base
,
datasize-append-lower-h
,
Used spec theorems:
min-max
/
min
array-splice
/buffer/
append-at1
array-splice
/buffer/
append-at2
Used simplifier rules:
nat
/
ge
nat
/
lez
min-max
/
min-0-left
nat
/
succ-01
nat-basic
/
l-05
nat-basic
/
succ
nat-basic
/
trans
nat-basic
/
lf
nat-basic
/
nls-fst
nat
/
le-one
nat
/
lels
nat
/
lep-02
array-splice
/buffer/
append-at2
nat
/
lels-03
nat
/
ls-le-simp
nat
/
le-def
array-splice
/buffer/
append-at1
array-splice
/buffer/
append-a
nat
/
les
nat-basic
/
lf-01
nat-basic
/
one-06
nat-basic
/
oz
nat-basic
/
l-01
nat
/
fle-01
nat-basic
/
eq-01
nat-basic
/
a
nat-basic
/
c
nat
/
lep
nat-basic
/
l
nat
/
eqle-one
nat-basic
/
f
nat-basic
/
z-01
nat
/
elim-sub