### Nuprl Lemma : list-decomp-no_repeats

[T:Type]. ∀[l1,l2,l3,l4:T List]. ∀[x:T].
((l1 l3 ∈ (T List)) ∧ (l2 l4 ∈ (T List))) supposing
((((l1 [x]) l2) ((l3 [x]) l4) ∈ (T List)) and
no_repeats(T;(l1 [x]) l2))

Proof

Definitions occuring in Statement :  no_repeats: no_repeats(T;l) append: as bs cons: [a b] nil: [] list: List uimplies: supposing a uall: [x:A]. B[x] and: P ∧ Q universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a and: P ∧ Q cand: c∧ B prop: iff: ⇐⇒ Q implies:  Q rev_implies:  Q all: x:A. B[x] subtype_rel: A ⊆B le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A squash: T top: Top true: True guard: {T} int_seg: {i..j-} lelt: i ≤ j < k decidable: Dec(P) or: P ∨ Q uiff: uiff(P;Q) satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] ge: i ≥  sq_type: SQType(T) select: L[n] cons: [a b] less_than: a < b no_repeats: no_repeats(T;l) nat: subtract: m
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation hypothesis sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality axiomEquality extract_by_obid isectElimination cumulativity hypothesisEquality isect_memberEquality because_Cache equalityTransitivity equalitySymmetry universeEquality independent_functionElimination lambdaFormation dependent_functionElimination applyEquality natural_numberEquality addEquality independent_isectElimination lambdaEquality imageElimination intEquality voidElimination voidEquality imageMemberEquality baseClosed applyLambdaEquality setElimination rename unionElimination pointwiseFunctionality promote_hyp baseApply closedConclusion dependent_pairFormation int_eqEquality computeAll dependent_set_memberEquality instantiate hyp_replacement multiplyEquality productEquality

Latex:
\mforall{}[T:Type].  \mforall{}[l1,l2,l3,l4:T  List].  \mforall{}[x:T].
((l1  =  l3)  \mwedge{}  (l2  =  l4))  supposing
((((l1  @  [x])  @  l2)  =  ((l3  @  [x])  @  l4))  and
no\_repeats(T;(l1  @  [x])  @  l2))

Date html generated: 2017_10_01-AM-08_39_11
Last ObjectModification: 2017_07_26-PM-04_27_23

Theory : list!

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