### Nuprl Lemma : update-tuple_wf

`∀[L:Type List]. ∀[n:ℕ]. ∀[x:tuple-type(L)].  ∀[y:L[n]]. (update-tuple(||L||;x;n;y) ∈ tuple-type(L)) supposing n < ||L||`

Proof

Definitions occuring in Statement :  update-tuple: `update-tuple(len;x;n;y)` tuple-type: `tuple-type(L)` select: `L[n]` length: `||as||` list: `T List` nat: `ℕ` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` 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` top: `Top` and: `P ∧ Q` prop: `ℙ` guard: `{T}` subtype_rel: `A ⊆r B` or: `P ∨ Q` select: `L[n]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` update-tuple: `update-tuple(len;x;n;y)` eq_int: `(i =z j)` subtract: `n - m` ifthenelse: `if b then t else f fi ` bfalse: `ff` cons: `[a / b]` colength: `colength(L)` decidable: `Dec(P)` 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)` bnot: `¬bb` assert: `↑b` le: `A ≤ B` int_upper: `{i...}` nequal: `a ≠ b ∈ T ` pi2: `snd(t)` pi1: `fst(t)`
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 select_wf intformeq_wf int_formula_prop_eq_lemma length_wf tuple-type_wf nat_wf equal-wf-T-base colength_wf_list less_than_transitivity1 less_than_irreflexivity list_wf list-cases tupletype_nil_lemma length_of_nil_lemma stuck-spread base_wf product_subtype_list spread_cons_lemma itermAdd_wf int_term_value_add_lemma 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 int_subtype_base decidable__equal_int tupletype_cons_lemma length_of_cons_lemma eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_int int_upper_subtype_nat false_wf nequal-le-implies zero-add int_upper_properties unit_wf2 null_nil_lemma subtype_rel-equal cons_wf nil_wf length-singleton select-cons-hd null_cons_lemma ifthenelse_wf null_wf assert_of_null non_neg_length add-subtract-cancel pi2_wf decidable__lt add-is-int-iff select-cons-tl
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry instantiate universeEquality because_Cache applyLambdaEquality applyEquality unionElimination baseClosed promote_hyp hypothesis_subsumption productElimination dependent_set_memberEquality addEquality cumulativity imageElimination equalityElimination productEquality independent_pairEquality pointwiseFunctionality baseApply closedConclusion

Latex:
\mforall{}[L:Type  List].  \mforall{}[n:\mBbbN{}].  \mforall{}[x:tuple-type(L)].
\mforall{}[y:L[n]].  (update-tuple(||L||;x;n;y)  \mmember{}  tuple-type(L))  supposing  n  <  ||L||

Date html generated: 2017_04_17-AM-09_29_32
Last ObjectModification: 2017_02_27-PM-05_30_28

Theory : tuples

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