### Nuprl Lemma : r-rational_wf

`∀[x:ℝ]. (r-rational(x) ∈ ℙ)`

Proof

Definitions occuring in Statement :  r-rational: `r-rational(x)` real: `ℝ` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` r-rational: `r-rational(x)` so_lambda: `λ2x.t[x]` nat_plus: `ℕ+` uimplies: `b supposing a` rneq: `x ≠ y` guard: `{T}` or: `P ∨ Q` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` decidable: `Dec(P)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  real_wf rless_wf int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_less_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformless_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__lt nat_plus_properties rless-int int-to-real_wf rdiv_wf req_wf nat_plus_wf exists_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin intEquality lambdaEquality hypothesis hypothesisEquality setElimination rename independent_isectElimination inrFormation dependent_functionElimination because_Cache productElimination independent_functionElimination natural_numberEquality unionElimination dependent_pairFormation int_eqEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[x:\mBbbR{}].  (r-rational(x)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-09_50_54
Last ObjectModification: 2016_01_17-AM-02_52_03

Theory : reals

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