Nuprl Lemma : 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]
, 
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
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
productEquality, 
hypothesisEquality, 
applyEquality, 
sqequalHypSubstitution, 
hypothesis, 
sqequalRule, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
cumulativity, 
universeEquality, 
isect_memberEquality, 
isectElimination, 
thin, 
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_53
Last ObjectModification:
2016_01_06-PM-05_28_58
Theory : core_2
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