Nuprl Lemma : l_subset_wf
∀[T:Type]. ∀[as,bs:T List]. (l_subset(T;as;bs) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
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_subset: l_subset(T;as;bs),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
all_wf,
l_member_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (l\_subset(T;as;bs) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-01_26_29
Last ObjectModification:
2018_09_26-PM-05_30_59
Theory : list_1
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