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Theorem INVR-step
⊦ INVR(C, N, V, n, n0, source, dest) ∧ INV(C, N, V, n, source) ∧ v ∈ C ∧ v ≠ dest → (¬ INVR(C -- v, N ∪ (succ(v) \ V), V ∪ succ(v), n, n0, source, dest) ↔ false)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
BFS
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 23
Proof steps: 57
Used lemmas:
INV-def
,
INVR-def
,
Used spec theorems:
graph
/
reach-rec-rev
graph
/
reachset-def
graph
/
reachls-def
graph
/
reach-trans
Used simplifier rules:
set-union
/
Difference
set-union
/
unin
nat-basic1
/
f
set-union
/
unc
set-union
/
una
set-union
/
Union
nat-basic2
/
l
nat
/
le-ls-simp
graph
/
reach-trans
nat
/
lels
nat-basic2
/
s
graph
/
reachset-mem-reach
nat-basic2
/
oz
nat
/
elim-pred-c
graph
/
reach-zero
nat-basic2
/
z
nat-basic2
/
l-01
nat
/
lep
set-basic
/
size-zero-01
set-basic
/
ne-01
nat-basic2
/
c
nat-basic2
/
a
graph
/
reach-succ
graph
/
reachset-one
set-union
/
One
set-union
/
del-rax
nat
/
elim-sub