Nuprl Lemma : small-reciprocal-real-ext
∀x:{x:ℝ| r0 < x} . ∃k:ℕ+. ((r1/r(k)) < x)
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rless: x < y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
sq_stable__rless,
small-reciprocal-real,
member: t ∈ T
Lemmas referenced :
small-reciprocal-real,
sq_stable__rless
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}x:\{x:\mBbbR{}| r0 < x\} . \mexists{}k:\mBbbN{}\msupplus{}. ((r1/r(k)) < x)
Date html generated:
2018_05_22-PM-01_50_19
Last ObjectModification:
2018_05_21-AM-00_08_47
Theory : reals
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