### 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: `ℕ` uall: `∀[x:A]. B[x]` top: `Top` so_apply: `x[s]` apply: `f a` sqequal: `s ~ t`
Definitions unfolded in proof :  tuple: `tuple(n;i.F[i])` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b 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: `ℙ` upto: `upto(n)` from-upto: `[n, m)` ifthenelse: `if b then t else f fi ` lt_int: `i <z 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: `n - m` btrue: `tt` decidable: `Dec(P)` or: `P ∨ Q` bool: `𝔹` unit: `Unit` it: `⋅` subtype_rel: `A ⊆r B` uiff: `uiff(P;Q)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` nat_plus: `ℕ+` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` pi1: `fst(t)` pi2: `snd(t)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` compose: `f o 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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