### Nuprl Lemma : coW2natinf_wf

`∀[n:ℕ]. ∀[w:coW(ℕ2;x.if (x =z 0) then Void else Unit fi )].  (coW2natinf(w;n) ∈ 𝔹)`

Proof

Definitions occuring in Statement :  coW2natinf: `coW2natinf(w;n)` coW: `coW(A;a.B[a])` int_seg: `{i..j-}` nat: `ℕ` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` bool: `𝔹` uall: `∀[x:A]. B[x]` unit: `Unit` member: `t ∈ T` natural_number: `\$n` void: `Void`
Definitions unfolded in proof :  ext-eq: `A ≡ B` lelt: `i ≤ j < k` assert: `↑b` bnot: `¬bb` sq_type: `SQType(T)` bfalse: `ff` uiff: `uiff(P;Q)` it: `⋅` unit: `Unit` bool: `𝔹` pi2: `snd(t)` coW-item: `coW-item(w;b)` or: `P ∨ Q` decidable: `Dec(P)` btrue: `tt` ifthenelse: `if b then t else f fi ` subtract: `n - m` eq_int: `(i =z j)` pi1: `fst(t)` coW2natinf: `coW2natinf(w;n)` guard: `{T}` subtype_rel: `A ⊆r B` so_apply: `x[s]` int_seg: `{i..j-}` so_lambda: `λ2x.t[x]` prop: `ℙ` and: `P ∧ Q` top: `Top` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` not: `¬A` uimplies: `b supposing a` ge: `i ≥ j ` false: `False` implies: `P `` Q` nat: `ℕ` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  nat_wf int_formula_prop_eq_lemma intformeq_wf int_seg_properties subtype_rel-equal it_wf neg_assert_of_eq_int assert-bnot bool_subtype_base subtype_base_sq bool_cases_sqequal equal_wf eqff_to_assert assert_of_eq_int eqtt_to_assert int_term_value_subtract_lemma int_formula_prop_not_lemma itermSubtract_wf intformnot_wf subtract_wf decidable__le bfalse_wf btrue_wf bool_wf subtype_rel_weakening coW-ext unit_wf2 eq_int_wf ifthenelse_wf int_seg_wf coW_wf less_than_wf ge_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf full-omega-unsat nat_properties
Rules used in proof :  cumulativity promote_hyp equalityElimination unionElimination productElimination functionEquality productEquality applyEquality because_Cache hypothesis_subsumption universeEquality instantiate equalitySymmetry equalityTransitivity axiomEquality independent_pairFormation voidEquality voidElimination isect_memberEquality dependent_functionElimination intEquality int_eqEquality lambdaEquality dependent_pairFormation independent_functionElimination approximateComputation independent_isectElimination natural_numberEquality lambdaFormation intWeakElimination sqequalRule rename setElimination hypothesis hypothesisEquality isectElimination sqequalHypSubstitution extract_by_obid thin cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[w:coW(\mBbbN{}2;x.if  (x  =\msubz{}  0)  then  Void  else  Unit  fi  )].    (coW2natinf(w;n)  \mmember{}  \mBbbB{})

Date html generated: 2018_07_29-AM-09_29_16
Last ObjectModification: 2018_07_27-PM-03_25_40

Theory : basic

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