Nuprl Lemma : polyconst_wf

[n:ℕ]. ∀[k:ℤ].  (polyconst(n;k) ∈ polyform(n))


Proof




Definitions occuring in Statement :  polyconst: polyconst(n;k) polyform: polyform(n) nat: uall: [x:A]. B[x] member: t ∈ T int:
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat: implies:  Q false: False ge: i ≥  uimplies: 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: polyconst: polyconst(n;k) polyform: polyform(n) eq_int: (i =z j) subtract: m ifthenelse: if then else fi  btrue: tt decidable: Dec(P) or: P ∨ Q subtype_rel: A ⊆B guard: {T} has-value: (a)↓ bool: 𝔹 unit: Unit it: uiff: uiff(P;Q) bfalse: ff sq_type: SQType(T) bnot: ¬bb assert: b nequal: a ≠ b ∈ 
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 less_than_transitivity1 le_weakening less_than_irreflexivity nat_wf value-type-has-value int-value-type polyform_wf le_wf polyform-value-type cons_wf nil_wf subtype_rel-equal list_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int
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 unionElimination because_Cache applyEquality callbyvalueReduce dependent_set_memberEquality equalityElimination productElimination promote_hyp instantiate cumulativity

Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[k:\mBbbZ{}].    (polyconst(n;k)  \mmember{}  polyform(n))



Date html generated: 2017_09_29-PM-06_00_22
Last ObjectModification: 2017_04_26-PM-02_04_55

Theory : integer!polynomials


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