Nuprl Lemma : rless-iff2-ext
∀x,y:ℝ. (x < y ⇐⇒ ∃n:ℕ+. (x n) + 4 < y n)
Proof
Definitions occuring in Statement :
rless: x < y,
real: ℝ,
nat_plus: ℕ+,
less_than: a < b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
pi1: fst(t),
rless-iff2
Lemmas referenced :
rless-iff2
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}x,y:\mBbbR{}. (x < y \mLeftarrow{}{}\mRightarrow{} \mexists{}n:\mBbbN{}\msupplus{}. (x n) + 4 < y n)
Date html generated:
2018_05_22-PM-01_21_12
Last ObjectModification:
2018_05_17-AM-09_19_35
Theory : reals
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