### Nuprl Lemma : div_mul_cancel

`∀[a:ℕ]. ∀[b:ℕ+].  (((a * b) ÷ b) = a ∈ ℤ)`

Proof

Definitions occuring in Statement :  nat_plus: `ℕ+` nat: `ℕ` uall: `∀[x:A]. B[x]` divide: `n ÷ m` multiply: `n * m` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` subtype_rel: `A ⊆r B` nat_plus: `ℕ+` int_nzero: `ℤ-o` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` nequal: `a ≠ b ∈ T ` not: `¬A` false: `False` guard: `{T}` ge: `i ≥ j ` 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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