Nuprl Lemma : no_repeats_union
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:T List]. no_repeats(T;as ⋃ bs) supposing no_repeats(T;as)
Proof
Definitions occuring in Statement :
l-union: 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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l-union: as ⋃ bs,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
prop: ℙ
Lemmas referenced :
list_induction,
no_repeats_wf,
reduce_wf,
list_wf,
insert_wf,
reduce_nil_lemma,
reduce_cons_lemma,
no_repeats-insert,
no_repeats_witness,
l-union_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
rename,
because_Cache,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:T List]. no\_repeats(T;as \mcup{} bs) supposing no\_repeats(T;as)
Date html generated:
2016_05_14-PM-03_25_07
Last ObjectModification:
2015_12_26-PM-06_22_18
Theory : decidable!equality
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