Nuprl Lemma : div_mul_cancel

[a:ℕ]. ∀[b:ℕ+].  (((a b) ÷ b) a ∈ ℤ)


Proof




Definitions occuring in Statement :  nat_plus: + nat: uall: [x:A]. B[x] divide: n ÷ m multiply: m int: equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T nat: subtype_rel: A ⊆B nat_plus: + int_nzero: -o so_lambda: λ2x.t[x] so_apply: x[s] uimplies: supposing a prop: all: x:A. B[x] implies:  Q nequal: a ≠ b ∈  not: ¬A false: False guard: {T} ge: i ≥  satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] top: Top and: P ∧ Q
Lemmas referenced :  nat_wf nat_plus_wf equal_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_eq_lemma int_formula_prop_and_lemma intformless_wf itermConstant_wf itermVar_wf intformeq_wf intformand_wf satisfiable-full-omega-tt nat_properties nat_plus_properties nequal_wf less_than_wf subtype_rel_sets div-cancel
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality applyEquality intEquality because_Cache lambdaEquality natural_numberEquality hypothesis independent_isectElimination setEquality lambdaFormation dependent_pairFormation int_eqEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality

Latex:
\mforall{}[a:\mBbbN{}].  \mforall{}[b:\mBbbN{}\msupplus{}].    (((a  *  b)  \mdiv{}  b)  =  a)



Date html generated: 2016_05_14-AM-07_24_19
Last ObjectModification: 2016_01_14-PM-10_01_58

Theory : int_2


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