Nuprl Lemma : no_repeats-concat
∀[T:Type]. ∀[ll:T List List].
(no_repeats(T;concat(ll))) supposing ((∀l∈ll.no_repeats(T;l)) and (∀l1,l2∈ll. l_disjoint(T;l1;l2)))
Proof
Definitions occuring in Statement :
pairwise: (∀x,y∈L. P[x; y]),
l_disjoint: l_disjoint(T;l1;l2),
l_all: (∀x∈L.P[x]),
no_repeats: no_repeats(T;l),
concat: concat(ll),
list: T List,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
cand: A c∧ B,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
no_repeats-concat-iff,
no_repeats_witness,
concat_wf,
l_all_wf,
list_wf,
no_repeats_wf,
l_member_wf,
pairwise_wf2,
l_disjoint_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
independent_isectElimination,
hypothesis,
independent_pairFormation,
independent_functionElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
instantiate,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[ll:T List List].
(no\_repeats(T;concat(ll))) supposing
((\mforall{}l\mmember{}ll.no\_repeats(T;l)) and
(\mforall{}l1,l2\mmember{}ll. l\_disjoint(T;l1;l2)))
Date html generated:
2016_05_14-PM-02_55_14
Last ObjectModification:
2015_12_26-PM-02_31_32
Theory : list_1
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