### Nuprl Lemma : uncurry-gen_wf

`∀[B:Type]. ∀[n:ℕ]. ∀[m:ℕn + 1]. ∀[A:ℕn ⟶ Type]. ∀[g:(k:ℕn ⟶ (A k)) ⟶ funtype(n - m;λx.(A (x + m));B)].`
`  (uncurry-gen(n) m g ∈ (k:ℕn ⟶ (A k)) ⟶ B)`

Proof

Definitions occuring in Statement :  uncurry-gen: `uncurry-gen(n)` funtype: `funtype(n;A;T)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` apply: `f a` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` subtract: `n - m` add: `n + m` natural_number: `\$n` 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` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` uiff: `uiff(P;Q)` decidable: `Dec(P)` or: `P ∨ Q` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` uncurry-gen: `uncurry-gen(n)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` funtype: `funtype(n;A;T)` primrec: `primrec(n;b;c)` less_than: `a < b` less_than': `less_than'(a;b)` true: `True` squash: `↓T` bfalse: `ff` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` le: `A ≤ B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  nat_properties full-omega-unsat 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 int_seg_wf funtype_wf int_seg_properties itermSubtract_wf int_term_value_subtract_lemma add-member-int_seg2 lelt_wf subtract_wf le_wf decidable__le intformnot_wf int_formula_prop_not_lemma decidable__equal_int subtype_base_sq set_subtype_base int_subtype_base intformeq_wf int_formula_prop_eq_lemma decidable__lt subtype_rel_self eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int subtype_rel-equal lt_int_wf assert_of_lt_int top_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_int nequal-le-implies itermAdd_wf int_term_value_add_lemma int_seg_subtype_nat false_wf add-member-int_seg1 nat_wf funtype-unroll assert_wf bnot_wf not_wf equal-wf-T-base zero-add add-is-int-iff add-associates add-swap add-commutes bool_cases iff_transitivity iff_weakening_uiff assert_of_bnot
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 approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation axiomEquality equalityTransitivity equalitySymmetry functionEquality because_Cache applyEquality functionExtensionality cumulativity productElimination dependent_set_memberEquality universeEquality unionElimination instantiate applyLambdaEquality hypothesis_subsumption equalityElimination lessCases baseClosed imageMemberEquality axiomSqEquality imageElimination promote_hyp addEquality baseApply closedConclusion

Latex:
\mforall{}[B:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[m:\mBbbN{}n  +  1].  \mforall{}[A:\mBbbN{}n  {}\mrightarrow{}  Type].
\mforall{}[g:(k:\mBbbN{}n  {}\mrightarrow{}  (A  k))  {}\mrightarrow{}  funtype(n  -  m;\mlambda{}x.(A  (x  +  m));B)].
(uncurry-gen(n)  m  g  \mmember{}  (k:\mBbbN{}n  {}\mrightarrow{}  (A  k))  {}\mrightarrow{}  B)

Date html generated: 2019_10_15-AM-11_04_15
Last ObjectModification: 2018_08_25-PM-02_15_10

Theory : bags

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