Nuprl Lemma : divides_anti_sym_n

[a,b:ℕ].  (a b ∈ ℤsupposing ((b a) and (a b))


Definitions occuring in Statement :  divides: a nat: uimplies: supposing a uall: [x:A]. B[x] int: equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a prop: nat: all: x:A. B[x] decidable: Dec(P) or: P ∨ Q divides: a exists: x:A. B[x] subtype_rel: A ⊆B ge: i ≥  satisfiable_int_formula: satisfiable_int_formula(fmla) false: False implies:  Q not: ¬A top: Top and: P ∧ Q nat_plus: + le: A ≤ B iff: ⇐⇒ Q rev_implies:  Q uiff: uiff(P;Q) less_than': less_than'(a;b) true: True subtract: 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

\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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