### Nuprl Lemma : rational-approx_wf

`∀[x:ℕ+ ⟶ ℤ]. ∀[n:ℕ+].  ((x within 1/n) ∈ ℝ)`

Proof

Definitions occuring in Statement :  rational-approx: `(x within 1/n)` real: `ℝ` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rational-approx: `(x within 1/n)` int_nzero: `ℤ-o` nat_plus: `ℕ+` nequal: `a ≠ b ∈ T ` not: `¬A` implies: `P `` Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` all: `∀x:A. B[x]` top: `Top` and: `P ∧ Q` prop: `ℙ`
Lemmas referenced :  nat_plus_wf int-to-real_wf nequal_wf equal_wf int_formula_prop_wf int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_formula_prop_eq_lemma int_formula_prop_and_lemma intformless_wf itermVar_wf itermConstant_wf itermMultiply_wf intformeq_wf intformand_wf satisfiable-full-omega-tt nat_plus_properties int-rdiv_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin dependent_set_memberEquality multiplyEquality natural_numberEquality setElimination rename hypothesisEquality hypothesis lambdaFormation independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality axiomEquality equalityTransitivity equalitySymmetry because_Cache functionEquality

Latex:
\mforall{}[x:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}].  \mforall{}[n:\mBbbN{}\msupplus{}].    ((x  within  1/n)  \mmember{}  \mBbbR{})

Date html generated: 2016_05_18-AM-07_29_51
Last ObjectModification: 2016_01_17-AM-01_59_52

Theory : reals

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