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Theorem copy-new-node
r0 ∈ H0, ¬ r0 ∈ map, H1 = H, map1 = map, copy-node-prepost(H0, H, map) ⊦ ⟪copy_node#(r0; r1, map, H)⟫ (copy-node-prepost(H0, H, map) ∧ H1 ⊆ H ∧ map1 ⊆ map ∧ r0 ∈ map ∧ map[r0] = r1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
copy-all-reachable-are-fresh
,
copy-no-effects
,
copy-term
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 55
Proof steps: 132
Used lemmas:
smaller
,
subset-smaller
,
copy-edges-prepost
,
copy-node-prepost
,
copy-edges-nonempty-term
,
in-propagate
,
copy-node
,
Used spec theorems:
ops-impl
/node-heap/
infinite-mem
heap
/node-heap/
uni-write
functions
/
dom-alloc
heap
/node-heap/
in-alloc
functions
/
inj
store
/ref-map/
At-other
nat-basic2
/
addex
heap
/node-heap/
subset
heap
/node-heap/
at-alloc
store
/ref-map/
Subset
heap
/node-heap/
disj
functions
/
closed
functions
/
closeds
Used simplifier rules:
functions
/
empty-node
node
/
elim
functions
/
ran-put-new
store+set
/ref-map-store+set-r/
dom-ins
functions
/
dom
set-basic
/refset/
sub-add-03
heap
/node-heap/
at-uni
heap
/node-heap/
disj-write
heap
/node-heap/
uni-alloc
heap
/node-heap/
disj-alloc
functions
/
closeds-empty
heap
/node-heap/
nonnull
store
/ref-map/
At-other
store
/ref-map/
in-neq
functions
/
inj-eq
heap
/node-heap/
at-alloc
nat
/
lels
store
/ref-map/
empty
nat
/
succ-01
store
/ref-map/
Size-insert
nat
/
lep
nat
/
ls-03
nat
/
le-ls-simp
nat
/
zero-01
nat-basic2
/
ax-08
nat
/
eq-02
nat
/
zero-02
nat
/
lels-03
nat
/
let
nat
/
lels-01
nat-basic1
/
ls-02
nat
/
elim-sub
nat-basic2
/
succ
nat-basic1
/
trans-1
nat-basic1
/
lf
nat-basic1
/
lf-01
nat
/
fle
nat
/
lels-02
nat-basic2
/
eq
nat-basic1
/
lf-02
nat-basic1
/
one
nat-basic2
/
l-01
nat
/
lep-02
nat-basic2
/
eq-01
nat-basic2
/
a
nat-basic2
/
c
nat-basic2
/
l
nat-basic2
/
one
nat-basic1
/
f
nat
/
le-add
heap
/node-heap/
in-alloc
store
/ref-map/
At-same
store
/ref-map/
insin
store
/ref-map/
At-in-out
store
/ref-map/
In-insert
heap
/node-heap/
disj-r
heap
/node-heap/
write-right
heap
/node-heap/
write-left
heap
/node-heap/
in-uni
functions
/
dom-write
heap
/node-heap/
disj-l
heap
/node-heap/
at-write
heap
/node-heap/
in-write-strong
functions
/
ran-in-heap-eq
functions
/
closed-succ
node
/
inj
functions
/
closed-succ-in