Nuprl Lemma : lg-acyclic-well-founded
∀[T:Type]. ∀g:LabeledGraph(T). (lg-acyclic(g) 
⇐⇒ SWellFounded(lg-edge(g;a;b)))
Proof
Definitions occuring in Statement : 
lg-acyclic: lg-acyclic(g)
, 
lg-edge: lg-edge(g;a;b)
, 
lg-size: lg-size(g)
, 
labeled-graph: LabeledGraph(T)
, 
strongwellfounded: SWellFounded(R[x; y])
, 
int_seg: {i..j-}
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
nat: ℕ
, 
guard: {T}
, 
prop: ℙ
, 
ge: i ≥ j 
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
so_apply: x[s]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uiff: uiff(P;Q)
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
squash: ↓T
, 
true: True
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
less_than: a < b
, 
strongwellfounded: SWellFounded(R[x; y])
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
sq_type: SQType(T)
, 
bnot: ¬bb
, 
assert: ↑b
, 
nequal: a ≠ b ∈ T 
, 
subtract: n - m
, 
lg-acyclic: lg-acyclic(g)
, 
lg-connected: lg-connected(g;a;b)
, 
infix_ap: x f y
Latex:
\mforall{}[T:Type].  \mforall{}g:LabeledGraph(T).  (lg-acyclic(g)  \mLeftarrow{}{}\mRightarrow{}  SWellFounded(lg-edge(g;a;b)))
Date html generated:
2016_05_17-AM-10_11_13
Last ObjectModification:
2016_01_18-AM-00_24_26
Theory : process-model
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