Nuprl Lemma : list_decomp

[T:Type]. ∀[L:T List].  [hd(L) tl(L)] supposing 0 < ||L||


Proof




Definitions occuring in Statement :  hd: hd(l) length: ||as|| tl: tl(l) cons: [a b] list: List less_than: a < b uimplies: supposing a uall: [x:A]. B[x] natural_number: $n 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 less_than: a < b squash: T less_than': less_than'(a;b) and: P ∧ Q cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] top: Top so_apply: x[s1;s2] sq_stable: SqStable(P) uiff: uiff(P;Q) le: A ≤ B not: ¬A 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)
Lemmas referenced :  nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf length_wf equal-wf-T-base nat_wf colength_wf_list list-cases length_of_nil_lemma reduce_tl_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 length_of_cons_lemma reduce_hd_cons_lemma reduce_tl_cons_lemma list_wf
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 cumulativity equalityTransitivity equalitySymmetry applyEquality because_Cache unionElimination imageElimination productElimination promote_hyp hypothesis_subsumption voidEquality applyLambdaEquality imageMemberEquality baseClosed addEquality dependent_set_memberEquality independent_pairFormation minusEquality intEquality instantiate universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].    L  \msim{}  [hd(L)  /  tl(L)]  supposing  0  <  ||L||



Date html generated: 2017_04_14-AM-08_47_52
Last ObjectModification: 2017_02_27-PM-03_34_39

Theory : list_0


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