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Theorem disj-union-rem
m ≤ # asar, n0 ≠ n1, n0 < m, n1 < m ⊦ disj(asar, 0, m) → (asar[n0] ∪ as) \ asar[n1] = asar[n0] ∪ (as \ asar[n1])
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
union-write
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 9
Used lemmas:
disj-in-both
,
Used spec theorems:
set-basic
/address-list-set/
Extension
set-union
/address-list-set/
unrax
set-union
/address-list-set/
Difference
Used simplifier rules:
nat
/
fle
nat-basic
/
f
set-union
/address-list-set/
unin
set-basic
/address-list-set/
size-zero-01
set-basic
/address-list-set/
ne-01
set-union
/address-list-set/
Difference
set-union
/address-list-set/
unin-01
set-union
/address-list-set/
una
set-union
/address-list-set/
unc