Nuprl Lemma : no_repeats-merge
∀[T:Type]. ∀[bs,as:T List]. (no_repeats(T;merge(as;bs))) supposing (sorted(as) and no_repeats(T;as)) supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
merge: merge(as;bs),
no_repeats: no_repeats(T;l),
sorted: sorted(L),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
merge: merge(as;bs),
all: ∀x:A. B[x],
top: Top,
guard: {T}
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
no_repeats_wf,
sorted_wf,
merge_wf,
reduce_nil_lemma,
no_repeats_witness,
reduce_cons_lemma,
s-insert-no-repeats,
sorted-merge,
s-insert_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}[bs,as:T List]. (no\_repeats(T;merge(as;bs))) supposing (sorted(as) and no\_repeats(T;as))
supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2016_05_15-PM-03_52_45
Last ObjectModification:
2015_12_27-PM-01_23_53
Theory : general
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