Nuprl Lemma : mul-list-append

[ns1,ns2:ℤ List].  (ns1 ns2)  ~ Π(ns1)  * Π(ns2) )


Proof




Definitions occuring in Statement :  mul-list: Π(ns)  append: as bs list: List uall: [x:A]. B[x] multiply: m int: 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 ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A top: Top and: P ∧ Q prop: subtype_rel: A ⊆B guard: {T} or: P ∨ Q 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] decidable: Dec(P) nil: [] it: so_lambda: λ2x.t[x] so_apply: x[s] sq_type: SQType(T) less_than: a < b squash: T less_than': less_than'(a;b) mul-list: Π(ns) 
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf list_wf equal-wf-base nat_wf list_subtype_base int_subtype_base less_than_transitivity1 less_than_irreflexivity list-cases list_ind_nil_lemma mul_list_nil_lemma product_subtype_list spread_cons_lemma colength_wf_list intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma equal-wf-T-base decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base decidable__equal_int list_ind_cons_lemma one-mul mul-list_wf reduce_cons_lemma mul-associates
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 dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom baseApply closedConclusion baseClosed applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality addEquality instantiate cumulativity imageElimination multiplyEquality

Latex:
\mforall{}[ns1,ns2:\mBbbZ{}  List].    (\mPi{}(ns1  @  ns2)    \msim{}  \mPi{}(ns1)    *  \mPi{}(ns2)  )



Date html generated: 2018_05_21-PM-06_57_17
Last ObjectModification: 2017_07_26-PM-04_59_35

Theory : general


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