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Theorem keyset-overwrite-add
m ≤ # kar ⊦ n < m → keyset(kar[n, ki], m) ++ kar[n] = keyset(kar, m) ++ ki
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
keyset-xchg
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 11
Used lemmas:
keyset-rec
,
keyset-base
,
key-set-write-other
,
Used spec theorems:
set-basic
/keyindex-set/
sw
Used simplifier rules:
nat
/
fle
nat
/
lez
nat-basic
/
zero-01
nat-basic
/
s-04
nat-basic
/
c
nat-basic
/
a
nat
/
succ-01
nat
/
lels
nat
/
ls-le-simp
array
/key-index-array/
Size-put
nat
/
anti
array
/key-index-array/
Put-same
nat-basic
/
succ
nat-basic
/
lf
nat-basic
/
f
nat
/
lels-02
array
/key-index-array/
Put-other
nat
/
lels-03
set-basic
/keyindex-set/
eq-04