### Nuprl Lemma : decidable__reducible

`∀n:ℕ. Dec(reducible(n))`

Proof

Definitions occuring in Statement :  reducible: `reducible(a)` nat: `ℕ` decidable: `Dec(P)` all: `∀x:A. B[x]`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` nat: `ℕ` decidable: `Dec(P)` or: `P ∨ Q` prop: `ℙ` uall: `∀[x:A]. B[x]` reducible: `reducible(a)` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` exists: `∃x:A. B[x]` so_lambda: `λ2x.t[x]` int_nzero: `ℤ-o` so_apply: `x[s]` rev_implies: `P `` Q` int_seg: `{i..j-}` gt: `i > j` nequal: `a ≠ b ∈ T ` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` not: `¬A` top: `Top` squash: `↓T` subtype_rel: `A ⊆r B` true: `True` guard: `{T}` nat_plus: `ℕ+` le: `A ≤ B` uiff: `uiff(P;Q)` less_than': `less_than'(a;b)` subtract: `n - m` divides: `b | a` lelt: `i ≤ j < k` cand: `A c∧ B` assoced: `a ~ b` sq_type: `SQType(T)`
Lemmas referenced :  nat_wf decidable__equal_int reducible_wf not_wf or_wf equal-wf-T-base exists_wf int_nzero_wf assoced_wf equal_wf int_seg_wf pos_mul_arg_bounds int_nzero_properties nat_properties decidable__lt satisfiable-full-omega-tt intformand_wf intformnot_wf intformless_wf itermConstant_wf itermMultiply_wf itermVar_wf intformeq_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_le_lemma int_formula_prop_wf absval_wf absval_pos decidable__le le_wf iff_weakening_equal squash_wf true_wf absval_mul intformimplies_wf intformor_wf int_formual_prop_imp_lemma int_formula_prop_or_lemma divisors_bound false_wf not-lt-2 not-equal-2 add_functionality_wrt_le add-associates add-zero zero-add le-add-cancel condition-implies-le add-commutes minus-add minus-zero less_than_wf multiply-is-int-iff absval-non-neg itermAdd_wf int_term_value_add_lemma lelt_wf divides_of_absvals divides_wf subtype_base_sq int_subtype_base int_seg_properties nequal_wf decidable__or decidable__exists_int_seg decidable__and2 decidable__not decidable__assoced decidable_functionality int_entire
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation introduction extract_by_obid hypothesis rename sqequalHypSubstitution dependent_functionElimination thin setElimination hypothesisEquality natural_numberEquality unionElimination inlFormation isectElimination because_Cache intEquality equalityTransitivity equalitySymmetry baseClosed independent_pairFormation productElimination sqequalRule lambdaEquality productEquality multiplyEquality addEquality independent_functionElimination independent_isectElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality computeAll applyEquality imageElimination equalityUniverse levelHypothesis dependent_set_memberEquality imageMemberEquality universeEquality minusEquality pointwiseFunctionality promote_hyp baseApply closedConclusion applyLambdaEquality instantiate cumulativity orFunctionality inrFormation

Latex:
\mforall{}n:\mBbbN{}.  Dec(reducible(n))

Date html generated: 2017_04_17-AM-09_42_44
Last ObjectModification: 2017_02_27-PM-05_38_03

Theory : num_thy_1

Home Index