### Nuprl Lemma : set-value-type

`∀[A:Type]. ∀[P:A ⟶ ℙ].  value-type({a:A| P[a]} ) supposing value-type(A)`

Proof

Definitions occuring in Statement :  value-type: `value-type(T)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` set: `{x:A| B[x]} ` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` so_apply: `x[s]` subtype_rel: `A ⊆r B` value-type: `value-type(T)` has-value: `(a)↓` prop: `ℙ`
Lemmas referenced :  subtype-value-type equal-wf-base base_wf value-type_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin setEquality hypothesisEquality applyEquality hypothesis because_Cache sqequalRule independent_isectElimination lambdaEquality setElimination rename isect_memberEquality axiomSqleEquality equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbP{}].    value-type(\{a:A|  P[a]\}  )  supposing  value-type(A)

Date html generated: 2016_05_13-PM-03_27_03
Last ObjectModification: 2015_12_26-AM-09_28_04

Theory : call!by!value_1

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