Nuprl Lemma : r-archimedean-rabs-ext
∀x:ℝ. ∃n:ℕ. (|x| ≤ r(n))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rabs: |x|,
int-to-real: r(n),
real: ℝ,
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Definitions unfolded in proof :
member: t ∈ T,
r-archimedean-rabs,
r-archimedean,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
uimplies: b supposing a,
canonical-bound-property,
rmax_lb
Lemmas referenced :
r-archimedean-rabs,
lifting-strict-spread,
strict4-spread,
r-archimedean,
canonical-bound-property,
rmax_lb
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}x:\mBbbR{}. \mexists{}n:\mBbbN{}. (|x| \mleq{} r(n))
Date html generated:
2017_10_03-AM-09_22_51
Last ObjectModification:
2017_07_28-AM-07_46_04
Theory : reals
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