Nuprl Lemma : lg-filter_wf
∀[T:Type]. ∀[P:T ⟶ 𝔹]. ∀[G:LabeledGraph(T)]. (lg-filter(P;G) ∈ LabeledGraph(T))
Proof
Definitions occuring in Statement :
lg-filter: lg-filter(P;G),
labeled-graph: LabeledGraph(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lg-filter: lg-filter(P;G),
labeled-graph: LabeledGraph(T),
lg-size: lg-size(g),
subtype_rel: A ⊆r B,
guard: {T},
nat: ℕ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[G:LabeledGraph(T)]. (lg-filter(P;G) \mmember{} LabeledGraph(T))
Date html generated:
2016_05_17-AM-10_09_02
Last ObjectModification:
2016_01_18-AM-00_22_46
Theory : process-model
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