Nuprl Lemma : down-closed_wf
∀[T:Type]. ∀[X:(T List) ⟶ ℙ]. (down-closed(T;X) ∈ ℙ)
Proof
Definitions occuring in Statement :
down-closed: down-closed(T;X),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
down-closed: down-closed(T;X),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
R-closed_wf,
list_wf,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[X:(T List) {}\mrightarrow{} \mBbbP{}]. (down-closed(T;X) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_09_59
Last ObjectModification:
2015_12_26-PM-07_54_28
Theory : fan-theorem
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