Nuprl Lemma : set-member_wf
∀[T:Type]. ∀[s:P(T)]. ∀[x:T]. ((x ∈ s) ∈ ℙ)
Proof
Definitions occuring in Statement :
set-member: (x ∈ s),
power-set: P(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
set-member: (x ∈ s),
power-set: P(T),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
equal_wf,
power-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
spreadEquality,
sqequalHypSubstitution,
hypothesisEquality,
lemma_by_obid,
isectElimination,
thin,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:P(T)]. \mforall{}[x:T]. ((x \mmember{} s) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_51_37
Last ObjectModification:
2015_12_26-AM-10_17_18
Theory : bar-induction
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