Nuprl Lemma : append_back_nil

[T:Type]. ∀[as:T List].  (as [] as)


Proof




Definitions occuring in Statement :  append: as bs nil: [] list: List uall: [x:A]. B[x] universe: Type 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 append: as bs so_lambda: so_lambda(x,y,z.t[x; y; z]) top: Top 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 :  list_wf nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list int_subtype_base list-cases 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 list_ind_cons_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut hypothesis axiomSqEquality Error :universeIsType,  extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule isect_memberEquality because_Cache universeEquality lambdaFormation setElimination rename intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination lambdaEquality dependent_functionElimination applyEquality 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{}[T:Type].  \mforall{}[as:T  List].    (as  @  []  \msim{}  as)



Date html generated: 2019_06_20-PM-00_39_19
Last ObjectModification: 2018_09_26-PM-02_05_49

Theory : list_0


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