Nuprl Lemma : set-wf
∀[A:Type]. ∀[P:A ⟶ ℙ]. ({a:A| P[a]} ∈ Type)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setEquality,
hypothesisEquality,
applyEquality,
hypothesis,
thin,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
isect_memberEquality,
isectElimination,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. (\{a:A| P[a]\} \mmember{} Type)
Date html generated:
2016_05_13-PM-03_07_00
Last ObjectModification:
2016_01_06-PM-05_28_47
Theory : core_2
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