Nuprl Lemma : coprime-exp1

a,b:ℤ.  (CoPrime(a,b)  (∀n:ℕCoPrime(a,b^n)))


Proof




Definitions occuring in Statement :  coprime: CoPrime(a,b) exp: i^n nat: all: x:A. B[x] implies:  Q int:
Definitions unfolded in proof :  all: x:A. B[x] implies:  Q member: t ∈ T top: Top prop: uall: [x:A]. B[x] nat: decidable: Dec(P) or: P ∨ Q uimplies: supposing a not: ¬A satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False and: P ∧ Q so_lambda: λ2x.t[x] so_apply: x[s] iff: ⇐⇒ Q rev_implies:  Q subtype_rel: A ⊆B exp: i^n bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) ifthenelse: if then else fi  bfalse: ff sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b
Lemmas referenced :  exp0_lemma coprime_wf exp_wf2 decidable__le subtract_wf full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermSubtract_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_subtract_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf le_wf set_wf less_than_wf primrec-wf2 nat_wf coprime_bezout_id decidable__equal_int intformeq_wf itermAdd_wf itermMultiply_wf int_formula_prop_eq_lemma int_term_value_add_lemma int_term_value_mul_lemma equal-wf-base int_subtype_base exists_wf primrec-unroll lt_int_wf bool_wf eqtt_to_assert assert_of_lt_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot coprime_prod
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut thin sqequalRule introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination isect_memberEquality voidElimination voidEquality hypothesis rename setElimination isectElimination hypothesisEquality dependent_set_memberEquality because_Cache natural_numberEquality unionElimination independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality independent_pairFormation productElimination baseApply closedConclusion baseClosed applyEquality equalityElimination equalityTransitivity equalitySymmetry promote_hyp instantiate cumulativity

Latex:
\mforall{}a,b:\mBbbZ{}.    (CoPrime(a,b)  {}\mRightarrow{}  (\mforall{}n:\mBbbN{}.  CoPrime(a,b\^{}n)))



Date html generated: 2018_05_21-PM-00_55_51
Last ObjectModification: 2018_05_19-AM-06_34_03

Theory : num_thy_1


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