### Nuprl Lemma : assoc_reln

`∀a,b:ℤ.  ((a | b) ∧ (b | a) `⇐⇒` a = ± b)`

Proof

Definitions occuring in Statement :  divides: `b | a` pm_equal: `i = ± j` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` int: `ℤ`
Definitions unfolded in proof :  all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` member: `t ∈ T` uall: `∀[x:A]. B[x]` prop: `ℙ` rev_implies: `P `` Q` pm_equal: `i = ± j` or: `P ∨ Q` divides: `b | a` exists: `∃x:A. B[x]` decidable: `Dec(P)` uimplies: `b supposing a` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` top: `Top` subtype_rel: `A ⊆r B`
Lemmas referenced :  divides_wf pm_equal_wf istype-int divides_anti_sym decidable__equal_int full-omega-unsat intformand_wf intformnot_wf intformeq_wf itermVar_wf itermMultiply_wf itermConstant_wf int_formula_prop_and_lemma istype-void int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_mul_lemma int_term_value_constant_lemma int_formula_prop_wf int_subtype_base itermMinus_wf int_term_value_minus_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :lambdaFormation_alt,  independent_pairFormation sqequalHypSubstitution productElimination thin sqequalRule Error :productIsType,  Error :universeIsType,  cut introduction extract_by_obid isectElimination hypothesisEquality hypothesis Error :inhabitedIsType,  dependent_functionElimination independent_functionElimination unionElimination Error :dependent_pairFormation_alt,  natural_numberEquality because_Cache independent_isectElimination approximateComputation Error :lambdaEquality_alt,  int_eqEquality Error :isect_memberEquality_alt,  voidElimination Error :equalityIsType4,  applyEquality multiplyEquality minusEquality

Latex:
\mforall{}a,b:\mBbbZ{}.    ((a  |  b)  \mwedge{}  (b  |  a)  \mLeftarrow{}{}\mRightarrow{}  a  =  \mpm{}  b)

Date html generated: 2019_06_20-PM-02_20_16
Last ObjectModification: 2018_10_03-AM-00_35_37

Theory : num_thy_1

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