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Theorem k-path
⊦ path(x, H) ↔ # x = 1 ∧ hd x ∈ H ∧ hd x ≠ null ∨ # x = 1 + 1 ∧ hd x ∈ H ∧ hd tl x ∈ H ∧ hd x ≠ null ∧ hd tl x ≠ null ∧ H[hd x].nxt = hd tl x ∨ # x ≥ 1 + 1 ∧ hd x ∈ H ∧ hd x ≠ null ∧ H[hd x].nxt = hd tl x ∧ path(tl x, H)
Type: A user defined theorem
Validity: The proof is valid.
Features: kodkodax,
Comment:
Used by:
reach-n-path-n
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 0
Proof steps: 4
Used lemmas:
path-first-in-H
,
path-cons
,
path-one
,
path-empty
,
Used spec theorems:
Used simplifier rules:
nat
/
ge
nat
/
le-num-04
nat
/
add-num-04
list
/reflist/
c
list
/reflist/
a
list
/reflist/
len-05
nat-basic2
/
succ
nat-basic2
/
one-03
list-data
/reflist/
l
nat-basic2
/
a
nat-basic2
/
c
nat
/
lep
list
/reflist/
e-01
list
/reflist/
app
list-data
/reflist/
size-01
list-data
/reflist/
elim-list-c