Nuprl Lemma : map-tuple-as-tuple

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


Proof




Definitions occuring in Statement :  select-tuple: x.n map-tuple: map-tuple(len;f;t) tuple: tuple(n;i.F[i]) n-tuple: n-tuple(n) nat: uall: [x:A]. B[x] top: Top apply: a 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: le: A ≤ B less_than': less_than'(a;b) so_lambda: λ2x.t[x] so_apply: x[s] map-tuple: map-tuple(len;f;t) eq_int: (i =z j) subtract: m ifthenelse: if then else fi  btrue: tt sq_type: SQType(T) guard: {T} decidable: Dec(P) or: P ∨ Q bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) bfalse: ff bnot: ¬bb assert: b select-tuple: x.n nequal: a ≠ b ∈  pi2: snd(t) tuple: tuple(n;i.F[i]) subtype_rel: A ⊆B cons: [a b] colength: colength(L) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] nil: [] less_than: a < b squash: T int_seg: {i..j-} pi1: fst(t) lelt: i ≤ j < k
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 n-tuple_wf top_wf n-tuple-decomp false_wf le_wf tuple-decomp subtype_base_sq unit_wf2 unit_subtype_base equal-unit it_wf decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int intformeq_wf int_formula_prop_eq_lemma eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_int upto_wf list_wf int_seg_wf nat_wf equal-wf-T-base colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases map_nil_lemma product_subtype_list spread_cons_lemma itermAdd_wf int_term_value_add_lemma set_subtype_base int_subtype_base decidable__equal_int map_cons_lemma int_seg_properties add-subtract-cancel
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 dependent_set_memberEquality because_Cache instantiate cumulativity equalityTransitivity equalitySymmetry unionElimination equalityElimination productElimination promote_hyp applyEquality hypothesis_subsumption applyLambdaEquality addEquality baseClosed imageElimination

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



Date html generated: 2017_04_17-AM-09_29_40
Last ObjectModification: 2017_02_27-PM-05_30_41

Theory : tuples


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