Nuprl Lemma : bottom-member-prop
∀[T:Type]. (⊥ ∈ T ∈ ℙ)
Proof
Definitions occuring in Statement : 
bottom: ⊥
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
prop: ℙ
Lemmas referenced : 
base-member-prop
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
baseClosed, 
hypothesis, 
sqequalRule, 
axiomEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  (\mbot{}  \mmember{}  T  \mmember{}  \mBbbP{})
Date html generated:
2016_05_13-PM-03_28_31
Last ObjectModification:
2016_01_14-PM-06_43_26
Theory : call!by!value_1
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