### Nuprl Lemma : i-approx_wf

`∀[n:ℕ+]. ∀[I:Interval].  (i-approx(I;n) ∈ Interval)`

Proof

Definitions occuring in Statement :  i-approx: `i-approx(I;n)` interval: `Interval` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` i-approx: `i-approx(I;n)` interval: `Interval` 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`
Lemmas referenced :  nat_plus_wf interval_wf radd_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 rsub_wf rccint_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin unionElimination lemma_by_obid isectElimination hypothesisEquality hypothesis because_Cache natural_numberEquality setElimination rename independent_isectElimination inrFormation dependent_functionElimination independent_functionElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll minusEquality axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[n:\mBbbN{}\msupplus{}].  \mforall{}[I:Interval].    (i-approx(I;n)  \mmember{}  Interval)

Date html generated: 2016_05_18-AM-08_39_25
Last ObjectModification: 2016_01_17-AM-02_23_35

Theory : reals

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