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Theorem copy-map
⊦ recursive-property (λ r0, r1, H0, H1, map0, map1. r0 ∈ map1 ∧ map1[r0] = r1, λ succ0, succ1, H0, H1, map0, map1. succ1 = apply(succ0, map1))
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: 35
Proof steps: 101
Used lemmas:
subset-trans
,
copy-some-node
,
copy-edges
,
copy-some-edges
,
strengthen-recursive-edges-property
,
strengthen-recursive-node-property
,
copy-monotone
,
copy-node
,
prove-recursion
,
Used spec theorems:
store
/ref-map/
Subset
store
/successors/
k-Extension
store
/successors/
In-insert
store
/successors/
At-other
functions
/
at-apply-succ
Used simplifier rules:
functions
/
empty-node
nat
/
elim-pred-c
nat-basic2
/
s
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz
heap
/node-heap/
in-alloc
node
/
elim
nat-basic1
/
ref-1
heap
/node-heap/
nonnull
store
/ref-map/
insin
store
/ref-map/
At-same
functions
/
apply-succ-empty
nat
/
pred-03
store
/ref-map/
sub-trans
functions
/
at-apply-succ
functions
/
in-apply-succ
store
/successors/
At-same
store
/ref-map/
subset-elem-eq-02
store
/successors/
Del-at
store
/successors/
Del-in