Nuprl Lemma : base-member-prop
∀[T:Type]. ∀t:Base. (t ∈ T ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
base_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
axiomEquality,
universeEquality,
isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}t:Base. (t \mmember{} T \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_28_29
Last ObjectModification:
2015_12_26-AM-09_27_25
Theory : call!by!value_1
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