Nuprl Lemma : l_member_wf
∀[T:Type]. ∀[x:T]. ∀[l:T List]. ((x ∈ l) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
l_member: (x ∈ l),
so_lambda: λ2x.t[x],
prop: ℙ,
cand: A c∧ B,
nat: ℕ,
uimplies: b supposing a,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
so_apply: x[s]
Lemmas referenced :
exists_wf,
nat_wf,
less_than_wf,
length_wf,
equal_wf,
select_wf,
sq_stable__le,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
productEquality,
setElimination,
rename,
because_Cache,
cumulativity,
hypothesisEquality,
independent_isectElimination,
natural_numberEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[l:T List]. ((x \mmember{} l) \mmember{} \mBbbP{})
Date html generated:
2017_04_14-AM-08_36_49
Last ObjectModification:
2017_02_27-PM-03_28_46
Theory : list_0
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