Nuprl Lemma : firstn_map

[f:Top]. ∀[n:ℕ]. ∀[l:Top List].  (firstn(n;map(f;l)) map(f;firstn(n;l)))


Proof




Definitions occuring in Statement :  firstn: firstn(n;as) map: map(f;as) list: List nat: uall: [x:A]. B[x] top: Top sqequal: t
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] not: ¬A all: x:A. B[x] top: Top and: P ∧ Q prop: decidable: Dec(P) or: P ∨ Q subtype_rel: A ⊆B guard: {T} firstn: firstn(n;as) 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] 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) bool: 𝔹 unit: Unit btrue: tt uiff: uiff(P;Q) ifthenelse: if then else fi  bfalse: ff
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 top_wf decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma nat_wf first0 map_wf map_nil_lemma equal-wf-T-base colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases list_ind_nil_lemma product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma le_wf equal_wf subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int map_cons_lemma lt_int_wf bool_wf equal-wf-base assert_wf le_int_wf bnot_wf list_ind_cons_lemma uiff_transitivity eqtt_to_assert assert_of_lt_int eqff_to_assert assert_functionality_wrt_uiff bnot_of_lt_int assert_of_le_int
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom unionElimination because_Cache functionExtensionality applyEquality promote_hyp hypothesis_subsumption productElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate cumulativity imageElimination baseApply closedConclusion equalityElimination

Latex:
\mforall{}[f:Top].  \mforall{}[n:\mBbbN{}].  \mforall{}[l:Top  List].    (firstn(n;map(f;l))  \msim{}  map(f;firstn(n;l)))



Date html generated: 2017_04_17-AM-08_00_43
Last ObjectModification: 2017_02_27-PM-04_30_45

Theory : list_1


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