Nuprl Lemma : lg-search_wf
∀[T:Type]. ∀[G:LabeledGraph(T)]. ∀[P:T ⟶ 𝔹]. (lg-search(G;x.P[x]) ∈ ℕlg-size(G)?)
Proof
Definitions occuring in Statement :
lg-search: lg-search(G;x.P[x]),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lg-search: lg-search(G;x.P[x]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
nat: ℕ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
lelt: i ≤ j < k,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
so_apply: x[s],
subtype_rel: A ⊆r B
Latex:
\mforall{}[T:Type]. \mforall{}[G:LabeledGraph(T)]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. (lg-search(G;x.P[x]) \mmember{} \mBbbN{}lg-size(G)?)
Date html generated:
2016_05_17-AM-10_18_38
Last ObjectModification:
2016_01_18-AM-00_21_00
Theory : process-model
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