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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