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
Home
Index