Nuprl Lemma : lg-acyclic-has-source
∀[T:Type]. ∀g:LabeledGraph(T). (∃i:ℕlg-size(g). (↑lg-is-source(g;i))) supposing (lg-acyclic(g) and 0 < lg-size(g))
Proof
Definitions occuring in Statement :
lg-is-source: lg-is-source(g;i),
lg-acyclic: lg-acyclic(g),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
assert: ↑b,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
lg-acyclic: lg-acyclic(g),
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
exists: ∃x:A. B[x],
lg-is-source: lg-is-source(g;i),
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
lg-edge: lg-edge(g;a;b),
assert: ↑b,
true: True,
cons: [a / b],
top: Top,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
pi1: fst(t),
nat_plus: ℕ+,
ge: i ≥ j ,
sq_exists: ∃x:{A| B[x]},
subtract: n - m
Latex:
\mforall{}[T:Type]
\mforall{}g:LabeledGraph(T)
(\mexists{}i:\mBbbN{}lg-size(g). (\muparrow{}lg-is-source(g;i))) supposing (lg-acyclic(g) and 0 < lg-size(g))
Date html generated:
2016_05_17-AM-10_10_54
Last ObjectModification:
2016_01_18-AM-00_23_11
Theory : process-model
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