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Theorem BFS-correct-if-reachable
reach(source, dest, n), ¬ reach<(source, dest, n) ⊦ ⟪BFS(source, dest; norfail)⟫ norfail = some(n)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: if reachable in n steps (but not fewer), then BFS returns this n.
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 43
Proof steps: 125
Used lemmas:
ADD-preserves-INV-INVR
,
decl-03
,
Used spec theorems:
set-union
/
ext
INV
/
INVR-def
INV
/
INV-def
graph
/
reachset-def
graph
/
reachls-def
Used simplifier rules:
nat-basic2
/
eq-01
nat
/
eq-01
nat
/
succ-01
nat
/
lels
nat
/
anti
INV
/
INV-nextlevel
INV
/
INVR-nextlevel
nat-basic2
/
l-02
nat-basic2
/
s
nat
/
lels-03
nat-basic2
/
eq
nat
/
lels-01
nat-basic1
/
ls-02
nat
/
elim-sub
nat-basic1
/
f
nat
/
lels-02
nat-basic2
/
z
nat
/
add-01
set-union
/
del-size
set-union
/
del-e-01
set-union
/
del-addeq-05
set-basic
/
in-04
nat-basic2
/
one-03
set-union
/
del-e-02
nat_or_fail
/
inj
nat-basic1
/
ref-1
graph
/
reachless-zero
graph
/
reach-zero
nat
/
zero
nat
/
ler
graph
/
reachset-one
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
oz
nat-basic2
/
succ
nat
/
zero-02
nat_or_fail
/
disj
set-basic
/
In-empty
set-basic
/
Size-empty
set-basic
/
size-zero-01
set-basic
/
ne-01
set-basic
/
size-zero-02
INV
/
INVR-init
INV
/
INV-init
set-basic
/
ne
set-basic
/
size-one-01
set-basic
/
one-size
set-union
/
One