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Theorem reach-n-path-n
⊦ n ≠ 0 → (reachable-n(H, n, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = n + 1))
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: 22
Proof steps: 63
Used lemmas:
k-path
,
path-one
,
path-cons
,
null-not-start-of-path
,
path-first-in-H
,
path-two
,
reachable-1-def
,
reachable-n-base
,
reachable-n-rec
,
Used spec theorems:
Used simplifier rules:
nat-basic2
/
oz
list-last
/reflist/
last-one
list
/reflist/
app
list-last
/reflist/
last-def
nat-basic2
/
succ
nat-basic2
/
z-01
nat
/
add-num-03
list-data
/reflist/
size-01
list-last
/reflist/
l-05
nat
/
le-num-04
nat
/
ge
list
/reflist/
c-07
nat
/
add-num-04
list-data
/reflist/
elim-list-c
nat
/
lep
list-data
/reflist/
l
nat-basic2
/
one-03
list
/reflist/
c-08
list-last
/reflist/
l-02
list
/reflist/
e-01
nat-basic2
/
c
nat-basic2
/
a
nat
/
add-num-01
list
/reflist/
len-02
list
/reflist/
len
list
/reflist/
c
list
/reflist/
a