### Nuprl Lemma : r-archimedean

`∀x:ℝ. ∃n:ℕ. ((r(-n) ≤ x) ∧ (x ≤ r(n)))`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` int-to-real: `r(n)` real: `ℝ` nat: `ℕ` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` and: `P ∧ Q` minus: `-n`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` and: `P ∧ Q` exists: `∃x:A. B[x]` uall: `∀[x:A]. B[x]` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` real: `ℝ` nat: `ℕ` nat_plus: `ℕ+` int_upper: `{i...}` so_apply: `x[s]` uimplies: `b supposing a` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` cand: `A c∧ B`
Lemmas referenced :  canonical-bound-property canonical-bound_wf subtype_rel_set int_upper_wf nat_wf all_wf nat_plus_wf le_wf absval_wf int_upper_subtype_nat false_wf rleq_wf int-to-real_wf real_wf
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality productElimination dependent_pairFormation isectElimination applyEquality natural_numberEquality sqequalRule lambdaEquality setElimination rename multiplyEquality independent_isectElimination dependent_set_memberEquality independent_pairFormation productEquality minusEquality because_Cache

Latex:
\mforall{}x:\mBbbR{}.  \mexists{}n:\mBbbN{}.  ((r(-n)  \mleq{}  x)  \mwedge{}  (x  \mleq{}  r(n)))

Date html generated: 2017_10_03-AM-08_55_13
Last ObjectModification: 2017_07_03-PM-05_27_11

Theory : reals

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