### Nuprl Lemma : polyvar_wf2

`∀[n:ℕ]. ∀[v:ℤ].  polyvar(n;v) ∈ polynom(n) supposing 0 < n`

Proof

Definitions occuring in Statement :  polyvar: `polyvar(n;v)` polynom: `polynom(n)` nat: `ℕ` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` 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` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` decidable: `Dec(P)` or: `P ∨ Q` polynom: `polynom(n)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` ifthenelse: `if b then t else f fi ` subtype_rel: `A ⊆r B` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` polyform-lead-nonzero: `polyform-lead-nonzero(n;p)` polyform: `polyform(n)` polyvar: `polyvar(n;v)` true: `True` has-value: `(a)↓` int_seg: `{i..j-}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` iff: `P `⇐⇒` Q` poly-zero: `poly-zero(n;p)`
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 decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int polyvar_wf intformeq_wf int_formula_prop_eq_lemma eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int nil_wf polynom_wf le_wf length_of_nil_lemma polyform-lead-nonzero_wf subtype_rel_list polyform_wf polynom_subtype_polyform decidable__lt top_wf value-type-has-value int-value-type decidable__equal_int polyform-value-type polyconst_wf cons_wf polyconst_wf2 length_of_cons_lemma reduce_hd_cons_lemma assert_wf poly-zero_wf nat_wf length_upto upto_wf int_seg_wf equal-wf-base all_wf list_wf assert-poly-zero not_wf polyconst-val list_subtype_base int_subtype_base false_wf null_cons_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination lambdaFormation natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry imageElimination productElimination because_Cache unionElimination equalityElimination applyEquality promote_hyp instantiate cumulativity dependent_set_memberEquality lessCases sqequalAxiom imageMemberEquality baseClosed callbyvalueReduce int_eqReduceTrueSq int_eqReduceFalseSq baseApply closedConclusion setEquality addLevel impliesFunctionality levelHypothesis

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[v:\mBbbZ{}].    polyvar(n;v)  \mmember{}  polynom(n)  supposing  0  <  n

Date html generated: 2017_09_29-PM-06_03_53
Last ObjectModification: 2017_04_26-PM-02_05_19

Theory : integer!polynomials

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