Nuprl Lemma : no_repeats-union-list

[T:Type]. ∀[eq:EqDecider(T)]. ∀[ll:T List List].  no_repeats(T;l-union-list(eq;ll))


Proof




Definitions occuring in Statement :  l-union-list: l-union-list(eq;ll) no_repeats: no_repeats(T;l) list: List deq: EqDecider(T) uall: [x:A]. B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T so_lambda: λ2x.t[x] so_apply: x[s] implies:  Q l-union-list: l-union-list(eq;ll) all: x:A. B[x] so_lambda: so_lambda(x,y,z.t[x; y; z]) top: Top so_apply: x[s1;s2;s3] uimplies: supposing a prop:
Lemmas referenced :  list_induction list_wf no_repeats_wf l-union-list_wf list_ind_nil_lemma no_repeats_nil list_ind_cons_lemma no_repeats_union no_repeats_witness deq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lemma_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis sqequalRule lambdaEquality independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality lambdaFormation rename independent_isectElimination because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[ll:T  List  List].    no\_repeats(T;l-union-list(eq;ll))



Date html generated: 2016_05_14-PM-03_25_15
Last ObjectModification: 2015_12_26-PM-06_22_24

Theory : decidable!equality


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