### Nuprl Lemma : qround_wf

`∀[r:ℚ]. ∀[k:ℕ+].  (qround(r;k) ∈ ℚ)`

Proof

Definitions occuring in Statement :  qround: `qround(r;k)` rationals: `ℚ` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` qround: `qround(r;k)` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q` prop: `ℙ` int_nzero: `ℤ-o` 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`
Lemmas referenced :  rationals_wf nat_plus_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 less_than_wf mul_nat_plus rounded-numerator_wf mk-rational_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality baseClosed hypothesis multiplyEquality setElimination rename lambdaFormation independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality computeAll axiomEquality equalityTransitivity equalitySymmetry because_Cache

Latex:
\mforall{}[r:\mBbbQ{}].  \mforall{}[k:\mBbbN{}\msupplus{}].    (qround(r;k)  \mmember{}  \mBbbQ{})

Date html generated: 2016_05_15-PM-10_38_01
Last ObjectModification: 2016_01_16-PM-09_37_01

Theory : rationals

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