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
Home
Index