### Nuprl Lemma : divides_anti_sym_n

`∀[a,b:ℕ].  (a = b ∈ ℤ) supposing ((b | a) and (a | b))`

Proof

Definitions occuring in Statement :  divides: `b | a` nat: `ℕ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` prop: `ℙ` nat: `ℕ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` divides: `b | a` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` ge: `i ≥ j ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` false: `False` implies: `P `` Q` not: `¬A` top: `Top` and: `P ∧ Q` nat_plus: `ℕ+` le: `A ≤ B` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` less_than': `less_than'(a;b)` true: `True` subtract: `n - m`
Lemmas referenced :  divides_wf nat_wf decidable__equal_int equal-wf-T-base int_subtype_base nat_properties 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 divisors_bound decidable__lt false_wf not-lt-2 not-equal-2 add_functionality_wrt_le add-associates add-zero zero-add le-add-cancel condition-implies-le add-commutes minus-add minus-zero less_than_wf intformle_wf int_formula_prop_le_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut hypothesis extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality sqequalRule isect_memberEquality axiomEquality because_Cache equalityTransitivity equalitySymmetry dependent_functionElimination natural_numberEquality unionElimination productElimination hyp_replacement Error :applyLambdaEquality,  intEquality baseApply closedConclusion baseClosed applyEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality voidElimination voidEquality independent_pairFormation computeAll dependent_set_memberEquality lambdaFormation independent_functionElimination addEquality minusEquality

Latex:
\mforall{}[a,b:\mBbbN{}].    (a  =  b)  supposing  ((b  |  a)  and  (a  |  b))

Date html generated: 2016_10_21-AM-11_07_37
Last ObjectModification: 2016_07_12-AM-06_00_22

Theory : num_thy_1

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