Nuprl Lemma : lg-size-nil
∀[T:Type]. ∀[g:LabeledGraph(T)]. uiff(lg-size(g) = 0 ∈ ℤ;g = lg-nil() ∈ LabeledGraph(T))
Proof
Definitions occuring in Statement :
lg-nil: lg-nil(),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
lg-size: lg-size(g),
lg-nil: lg-nil(),
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
labeled-graph: LabeledGraph(T),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
or: P ∨ Q,
cons: [a / b],
top: Top,
ge: i ≥ j ,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
guard: {T}
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. uiff(lg-size(g) = 0;g = lg-nil())
Date html generated:
2016_05_17-AM-10_08_52
Last ObjectModification:
2016_01_18-AM-00_22_50
Theory : process-model
Home
Index