Nuprl Lemma : bar-wf-base
∀[T:Type]. bar(T) ∈ Type supposing T ⊆r Base
Proof
Definitions occuring in Statement : 
bar: bar(T)
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
base: Base
, 
universe: Type
Definitions unfolded in proof : 
bar: bar(T)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
Lemmas referenced : 
base_wf, 
subtype_rel_wf, 
partial_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
because_Cache, 
universeEquality
Latex:
\mforall{}[T:Type].  bar(T)  \mmember{}  Type  supposing  T  \msubseteq{}r  Base
Date html generated:
2016_05_15-PM-10_03_41
Last ObjectModification:
2016_01_05-PM-06_24_33
Theory : bar!type
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