Nuprl Lemma : l_intersection_nil
∀[A:Type]. ∀eq:EqDecider(A). ∀L:A List. (l_intersection(eq;L;[]) = [] ∈ (A List))
Proof
Definitions occuring in Statement :
l_intersection: l_intersection(eq;L1;L2),
nil: [],
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
l_intersection: l_intersection(eq;L1;L2),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
deq_member_nil_lemma,
filter-bfalse,
subtype_rel_list,
top_wf,
nil_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
lambdaFormation,
isectElimination,
hypothesisEquality,
applyEquality,
independent_isectElimination,
lambdaEquality,
because_Cache,
axiomEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}eq:EqDecider(A). \mforall{}L:A List. (l\_intersection(eq;L;[]) = [])
Date html generated:
2016_05_14-PM-03_32_33
Last ObjectModification:
2015_12_26-PM-06_01_06
Theory : decidable!equality
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