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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