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Theorem insert-rec-correct
¬ a ∈ s, s = abs(T1, T2, h1, h2), inv(T1, h1), inv(T2, h2), disj(T1, T2) ⊦ [insert_rec(a, h1, h2; T1, T2)] (s ++ a = abs(T1, T2, h1, h2) ∧ inv(T1, h1) ∧ inv(T2, h2) ∧ disj(T1, T2))
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: 17
Proof steps: 75
Used lemmas:
abs-sym
,
hash-same
,
disj-reduce
,
inv-reduce
,
less
,
size
,
disj-neq
,
at-put
,
hash-given
,
in-abs
,
Used spec theorems:
set-basic
/
Extension
Used simplifier rules:
nat
/
pred-03
nat
/
elim-pred-c
nat-basic2
/
oz
slot
/
elim
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
a
nat-basic2
/
c
array
/table/
Size-put
array
/table/
cngetput
set-basic
/
rax
nat-basic1
/
f
array
/table/
Put-other
slot
/
disj
slot
/
sel
slot
/
inj