### Nuprl Lemma : int_pi_det_fun_wf

`∀[i:ℤ]. ((i)ℤ-det-fun ∈ detach_fun(|ℤ-rng|;(i)ℤ-rng))`

Proof

Definitions occuring in Statement :  int_pi_det_fun: `(i)ℤ-det-fun` int_ring: `ℤ-rng` princ_ideal: `(a)r` rng_car: `|r|` detach_fun: `detach_fun(T;A)` uall: `∀[x:A]. B[x]` member: `t ∈ T` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` int_ring: `ℤ-rng` rng_car: `|r|` pi1: `fst(t)` int_pi_det_fun: `(i)ℤ-det-fun` princ_ideal: `(a)r` detach_fun: `detach_fun(T;A)` rng_times: `*` pi2: `snd(t)` infix_ap: `x f y` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` so_apply: `x[s]` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` not: `¬A` top: `Top` int_nzero: `ℤ-o` nequal: `a ≠ b ∈ T ` squash: `↓T` true: `True`
Lemmas referenced :  eq_int_wf bool_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int eqtt_to_assert assert_of_eq_int all_wf iff_wf exists_wf equal-wf-base int_subtype_base assert_wf decidable__equal_int satisfiable-full-omega-tt intformand_wf intformnot_wf intformeq_wf itermVar_wf itermConstant_wf itermMultiply_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_formula_prop_wf div_rem_sum nequal_wf mul-commutes squash_wf true_wf divide-exact iff_weakening_equal add-is-int-iff itermAdd_wf int_term_value_add_lemma false_wf multiply-is-int-iff
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule dependent_set_memberEquality lambdaEquality extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality natural_numberEquality hypothesis lambdaFormation unionElimination equalityElimination productElimination independent_isectElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity independent_functionElimination because_Cache voidElimination remainderEquality intEquality applyEquality baseApply closedConclusion baseClosed functionExtensionality axiomEquality independent_pairFormation int_eqEquality isect_memberEquality voidEquality computeAll addLevel impliesFunctionality divideEquality multiplyEquality imageElimination universeEquality equalityUniverse levelHypothesis imageMemberEquality hyp_replacement applyLambdaEquality pointwiseFunctionality rename

Latex:
\mforall{}[i:\mBbbZ{}].  ((i)\mBbbZ{}-det-fun  \mmember{}  detach\_fun(|\mBbbZ{}-rng|;(i)\mBbbZ{}-rng))

Date html generated: 2017_10_01-AM-08_18_40
Last ObjectModification: 2017_02_28-PM-02_03_32

Theory : rings_1

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