Nuprl Lemma : has-value_wf-bar
∀[T:Type]. ∀[a:bar(T)]. ((a)↓ ∈ ℙ) supposing value-type(T)
Proof
Definitions occuring in Statement :
bar: bar(T),
value-type: value-type(T),
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
bar: bar(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
value-type_wf,
partial_wf,
has-value_wf-partial
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:bar(T)]. ((a)\mdownarrow{} \mmember{} \mBbbP{}) supposing value-type(T)
Date html generated:
2016_05_15-PM-10_03_45
Last ObjectModification:
2016_01_05-PM-06_25_41
Theory : bar!type
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