Nuprl Lemma : rabs-strict-ub
∀a:ℝ. ((r0 ≤ a) ⇒ (∀x:ℝ. (a < |x| ⇐⇒ (a < x) ∨ (a < -(x)))))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rless: x < y,
rabs: |x|,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
guard: {T},
uimplies: b supposing a,
rneq: x ≠ y,
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Latex:
\mforall{}a:\mBbbR{}. ((r0 \mleq{} a) {}\mRightarrow{} (\mforall{}x:\mBbbR{}. (a < |x| \mLeftarrow{}{}\mRightarrow{} (a < x) \mvee{} (a < -(x)))))
Date html generated:
2020_05_20-AM-11_03_04
Last ObjectModification:
2019_11_11-PM-09_11_46
Theory : reals
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