Nuprl Lemma : list-deq_wf1

[A:Type]. ∀[eq:A ⟶ A ⟶ 𝔹].  (list-deq(eq) ∈ (A List) ⟶ (A List) ⟶ 𝔹)


Proof




Definitions occuring in Statement :  list-deq: list-deq(eq) list: List bool: 𝔹 uall: [x:A]. B[x] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T list-deq: list-deq(eq) 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 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 bool: 𝔹 unit: Unit btrue: tt band: p ∧b q ifthenelse: if then else fi  bfalse: ff
Lemmas referenced :  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 null_wf 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 list_ind_wf bool_wf bfalse_wf eqtt_to_assert list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaEquality thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination independent_functionElimination voidElimination dependent_functionElimination axiomEquality equalityTransitivity equalitySymmetry because_Cache applyEquality unionElimination isect_memberEquality voidEquality promote_hyp hypothesis_subsumption productElimination applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate cumulativity functionExtensionality equalityElimination functionEquality universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}[eq:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbB{}].    (list-deq(eq)  \mmember{}  (A  List)  {}\mrightarrow{}  (A  List)  {}\mrightarrow{}  \mBbbB{})



Date html generated: 2018_05_21-PM-00_19_44
Last ObjectModification: 2018_05_19-AM-07_00_00

Theory : list_0


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