Nuprl Lemma : list-valueall-type

[T:Type]. valueall-type(T List) supposing valueall-type(T)


Proof




Definitions occuring in Statement :  list: List valueall-type: valueall-type(T) uimplies: supposing a uall: [x:A]. B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a valueall-type: valueall-type(T) all: x:A. B[x] implies:  Q prop: has-value: (a)↓ nat: false: False ge: i ≥  guard: {T} subtype_rel: A ⊆B or: P ∨ Q cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] top: Top 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 evalall: evalall(t) has-valueall: has-valueall(a)
Lemmas referenced :  list_wf equal_wf equal-wf-base base_wf valueall-type_wf nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list list-cases 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 subtract_wf not-ge-2 less-iff-le minus-minus add-swap subtype_base_sq set_subtype_base int_subtype_base has-value_wf_base is-exception_wf valueall-type-has-valueall
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution equalityTransitivity hypothesis equalitySymmetry thin extract_by_obid isectElimination cumulativity hypothesisEquality lambdaFormation dependent_functionElimination independent_functionElimination sqequalRule axiomSqleEquality because_Cache isect_memberEquality universeEquality setElimination rename intWeakElimination natural_numberEquality independent_isectElimination voidElimination lambdaEquality applyEquality unionElimination promote_hyp hypothesis_subsumption productElimination voidEquality applyLambdaEquality imageMemberEquality baseClosed imageElimination addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate divergentSqle sqleReflexivity callbyvalueReduce

Latex:
\mforall{}[T:Type].  valueall-type(T  List)  supposing  valueall-type(T)



Date html generated: 2017_04_14-AM-08_34_12
Last ObjectModification: 2017_02_27-PM-03_21_55

Theory : list_0


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