### Nuprl Lemma : i-closed-finite-rep

`∀I:Interval. (i-closed(I) `` i-finite(I) `` (∃a,b:ℝ. (I = [a, b] ∈ Interval)))`

Proof

Definitions occuring in Statement :  rccint: `[l, u]` i-closed: `i-closed(I)` i-finite: `i-finite(I)` interval: `Interval` real: `ℝ` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` implies: `P `` Q` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` interval: `Interval` i-finite: `i-finite(I)` isl: `isl(x)` assert: `↑b` ifthenelse: `if b then t else f fi ` btrue: `tt` i-closed: `i-closed(I)` outl: `outl(x)` bnot: `¬bb` bor: `p ∨bq` bfalse: `ff` and: `P ∧ Q` exists: `∃x:A. B[x]` member: `t ∈ T` rccint: `[l, u]` uall: `∀[x:A]. B[x]` prop: `ℙ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` top: `Top` false: `False`
Lemmas referenced :  rccint_wf equal_wf interval_wf subtype_rel_product real_wf top_wf subtype_rel_union exists_wf i-finite_wf i-closed_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation sqequalHypSubstitution productElimination thin unionElimination sqequalRule dependent_pairFormation hypothesisEquality because_Cache cut hypothesis lemma_by_obid isectElimination independent_pairEquality inlEquality voidEquality applyEquality unionEquality lambdaEquality independent_isectElimination voidElimination isect_memberEquality

Latex:
\mforall{}I:Interval.  (i-closed(I)  {}\mRightarrow{}  i-finite(I)  {}\mRightarrow{}  (\mexists{}a,b:\mBbbR{}.  (I  =  [a,  b])))

Date html generated: 2016_05_18-AM-08_48_23
Last ObjectModification: 2015_12_27-PM-11_45_48

Theory : reals

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