### Nuprl Lemma : sq_exists_wf

`∀[A:Type]. ∀[B:A ⟶ ℙ].  (∃a:{A| B[a]} ∈ ℙ)`

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` sq_exists: `∃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` sq_exists: `∃x:{A| B[x]}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` prop: `ℙ`
Lemmas referenced :  set_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality applyEquality hypothesis universeEquality axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity isect_memberEquality because_Cache

Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  \mBbbP{}].    (\mexists{}a:\{A|  B[a]\}  \mmember{}  \mBbbP{})

Date html generated: 2016_05_13-PM-03_06_59
Last ObjectModification: 2016_01_06-PM-05_28_48

Theory : core_2

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