### Nuprl Lemma : append-tuple-zero

`∀[L:Type List]. ∀[x:tuple-type(L)]. ∀[y:Top].  (append-tuple(||L||;0;x;y) ~ if (||L|| =z 0) then y else x fi )`

Proof

Definitions occuring in Statement :  append-tuple: `append-tuple(n;m;x;y)` tuple-type: `tuple-type(L)` length: `||as||` list: `T List` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` uall: `∀[x:A]. B[x]` top: `Top` natural_number: `\$n` universe: `Type` sqequal: `s ~ t`
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` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` append-tuple: `append-tuple(n;m;x;y)` le_int: `i ≤z j` lt_int: `i <z j` bnot: `¬bb` ifthenelse: `if b then t else f fi ` bfalse: `ff` eq_int: `(i =z j)` btrue: `tt` subtract: `n - m` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` 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` uiff: `uiff(P;Q)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` le: `A ≤ B` assert: `↑b` true: `True`
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 tuple-type_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list_wf list-cases tupletype_nil_lemma length_of_nil_lemma unit_wf2 product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma 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 null_wf bool_wf uiff_transitivity assert_wf eqtt_to_assert assert_of_null le_int_wf length_wf assert_of_le_int eq_int_wf assert_of_eq_int iff_transitivity bnot_wf not_wf iff_weakening_uiff eqff_to_assert assert_of_bnot non_neg_length lt_int_wf assert_functionality_wrt_uiff bnot_of_le_int assert_of_lt_int add-is-int-iff false_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_int squash_wf true_wf add_functionality_wrt_eq iff_weakening_equal add-subtract-cancel
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality sqequalRule independent_pairFormation computeAll independent_functionElimination sqequalAxiom instantiate universeEquality applyEquality because_Cache unionElimination promote_hyp hypothesis_subsumption productElimination equalityTransitivity equalitySymmetry applyLambdaEquality dependent_set_memberEquality addEquality baseClosed cumulativity imageElimination equalityElimination impliesFunctionality pointwiseFunctionality baseApply closedConclusion imageMemberEquality

Latex:
\mforall{}[L:Type  List].  \mforall{}[x:tuple-type(L)].  \mforall{}[y:Top].
(append-tuple(||L||;0;x;y)  \msim{}  if  (||L||  =\msubz{}  0)  then  y  else  x  fi  )

Date html generated: 2017_04_17-AM-09_30_07
Last ObjectModification: 2017_02_27-PM-05_31_02

Theory : tuples

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