Nuprl Lemma : no_repeats-intersection
∀[A:Type]. ∀eq:EqDecider(A). ∀L1,L2:A List. (no_repeats(A;L1) ⇒ no_repeats(A;(L1 ⋂ L2)))
Proof
Definitions occuring in Statement :
l_intersection: (L1 ⋂ L2),
no_repeats: no_repeats(T;l),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
l_intersection: (L1 ⋂ L2),
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
no_repeats_filter,
deq-member_wf,
no_repeats_wf,
list_wf,
deq_wf,
no_repeats_witness,
l_intersection_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
cumulativity,
hypothesis,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}eq:EqDecider(A). \mforall{}L1,L2:A List. (no\_repeats(A;L1) {}\mRightarrow{} no\_repeats(A;(L1 \mcap{} L2)))
Date html generated:
2018_05_21-PM-00_51_31
Last ObjectModification:
2017_10_11-PM-02_12_24
Theory : decidable!equality
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