Nuprl Lemma : no_repeats_list-diff
∀[T:Type]. ∀[L1,L2:T List]. ∀[eq:EqDecider(T)]. no_repeats(T;L1-L2) supposing no_repeats(T;L1)
Proof
Definitions occuring in Statement :
list-diff: as-bs,
no_repeats: no_repeats(T;l),
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
list-diff: as-bs,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
no_repeats_filter,
bnot_wf,
deq-member_wf,
list-diff_wf,
no_repeats_wf,
deq_wf,
list_wf,
no_repeats_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
independent_isectElimination,
because_Cache,
universeEquality,
isect_memberFormation,
introduction,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[L1,L2:T List]. \mforall{}[eq:EqDecider(T)]. no\_repeats(T;L1-L2) supposing no\_repeats(T;L1)
Date html generated:
2016_05_14-PM-03_30_14
Last ObjectModification:
2015_12_26-PM-06_02_44
Theory : decidable!equality
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