Nuprl Lemma : rev-append-rev-append

[as:Top List]. ∀[bs,cs:Top].  (rev(rev(as) bs) cs rev(bs) as cs)


Proof




Definitions occuring in Statement :  rev-append: rev(as) bs append: as bs list: List uall: [x:A]. B[x] top: Top sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T all: x:A. B[x] nat: implies:  Q false: False ge: i ≥  guard: {T} uimplies: supposing a prop: subtype_rel: A ⊆B or: P ∨ Q top: Top append: as bs so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3] cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] squash: T sq_stable: SqStable(P) uiff: uiff(P;Q) and: P ∧ Q le: A ≤ B not: ¬A less_than': less_than'(a;b) true: True decidable: Dec(P) iff: ⇐⇒ Q rev_implies:  Q subtract: m nil: [] it: so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b
Lemmas referenced :  nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf top_wf equal-wf-T-base nat_wf colength_wf_list list_wf list-cases rev_app_nil_lemma list_ind_nil_lemma product_subtype_list spread_cons_lemma sq_stable__le le_antisymmetry_iff add_functionality_wrt_le add-associates add-zero zero-add le-add-cancel decidable__le false_wf not-le-2 condition-implies-le minus-add minus-one-mul minus-one-mul-top add-commutes le_wf equal_wf subtract_wf not-ge-2 less-iff-le minus-minus add-swap subtype_base_sq set_subtype_base int_subtype_base rev_app_cons_lemma list_ind_cons_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination sqequalRule lambdaEquality dependent_functionElimination isect_memberEquality sqequalAxiom applyEquality because_Cache unionElimination voidEquality promote_hyp hypothesis_subsumption productElimination applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality equalityTransitivity equalitySymmetry intEquality instantiate cumulativity

Latex:
\mforall{}[as:Top  List].  \mforall{}[bs,cs:Top].    (rev(rev(as)  +  bs)  +  cs  \msim{}  rev(bs)  +  as  @  cs)



Date html generated: 2017_04_14-AM-08_35_12
Last ObjectModification: 2017_02_27-PM-03_27_17

Theory : list_0


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