Nuprl Lemma : map-tuple-tuple

[n:ℕ]. ∀[f,G:Top].  (map-tuple(n;f;tuple(n;i.G[i])) tuple(n;i.f G[i]))


Proof




Definitions occuring in Statement :  map-tuple: map-tuple(len;f;t) tuple: tuple(n;i.F[i]) nat: uall: [x:A]. B[x] top: Top so_apply: x[s] apply: a sqequal: t
Definitions unfolded in proof :  tuple: tuple(n;i.F[i]) 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: upto: upto(n) from-upto: [n, m) ifthenelse: if then else fi  lt_int: i <j bfalse: ff so_lambda: so_lambda(x,y,z.t[x; y; z]) so_apply: x[s1;s2;s3] map-tuple: map-tuple(len;f;t) eq_int: (i =z j) subtract: m btrue: tt decidable: Dec(P) or: P ∨ Q bool: 𝔹 unit: Unit it: subtype_rel: A ⊆B uiff: uiff(P;Q) iff: ⇐⇒ Q rev_implies:  Q nat_plus: + sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b nequal: a ≠ b ∈  pi1: fst(t) pi2: snd(t) so_lambda: λ2x.t[x] so_apply: x[s] compose: g
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 top_wf map_nil_lemma list_ind_nil_lemma decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma eq_int_wf bool_wf uiff_transitivity equal-wf-base int_subtype_base assert_wf eqtt_to_assert assert_of_eq_int intformeq_wf int_formula_prop_eq_lemma iff_transitivity bnot_wf not_wf iff_weakening_uiff eqff_to_assert assert_of_bnot equal_wf nat_wf map_cons_lemma list_ind_cons_lemma le_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int upto_decomp2 null-map null-upto map-map
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep 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 independent_pairFormation computeAll independent_functionElimination sqequalAxiom because_Cache unionElimination equalityElimination baseApply closedConclusion baseClosed applyEquality equalityTransitivity equalitySymmetry productElimination impliesFunctionality dependent_set_memberEquality promote_hyp instantiate cumulativity

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f,G:Top].    (map-tuple(n;f;tuple(n;i.G[i]))  \msim{}  tuple(n;i.f  G[i]))



Date html generated: 2017_04_17-AM-09_29_42
Last ObjectModification: 2017_02_27-PM-05_30_11

Theory : tuples


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