Nuprl Lemma : rless-iff2
∀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 :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
real: ℝ,
so_apply: x[s],
rless: x < y,
sq_exists: ∃x:{A| B[x]},
exists: ∃x:A. B[x]
Lemmas referenced :
rless_wf,
exists_wf,
nat_plus_wf,
less_than_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
addEquality,
applyEquality,
setElimination,
rename,
natural_numberEquality,
dependent_pairFormation,
productElimination,
dependent_set_memberFormation
Latex:
\mforall{}x,y:\mBbbR{}. (x < y \mLeftarrow{}{}\mRightarrow{} \mexists{}n:\mBbbN{}\msupplus{}. (x n) + 4 < y n)
Date html generated:
2016_05_18-AM-07_04_07
Last ObjectModification:
2015_12_28-AM-00_35_11
Theory : reals
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