### 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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