Nuprl Lemma : l_intersection_wf
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[L1,L2:A List]. (l_intersection(eq;L1;L2) ∈ A List)
Proof
Definitions occuring in Statement :
l_intersection: l_intersection(eq;L1;L2),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
l_intersection: l_intersection(eq;L1;L2),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
filter_wf5,
l_member_wf,
deq-member_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
hypothesis,
setElimination,
rename,
because_Cache,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[L1,L2:A List]. (l\_intersection(eq;L1;L2) \mmember{} A List)
Date html generated:
2016_05_14-PM-03_32_27
Last ObjectModification:
2015_12_26-PM-06_01_21
Theory : decidable!equality
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