Nuprl Lemma : real-vec-sep-iff2
∀n:ℕ. ∀a,b:ℝ^n. (b ≠ a ⇐⇒ d(b;b) < d(b;a))
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
real-vec-dist: d(x;y),
real-vec: ℝ^n,
rless: x < y,
nat: ℕ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
real-vec-sep: a ≠ b,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b:\mBbbR{}\^{}n. (b \mneq{} a \mLeftarrow{}{}\mRightarrow{} d(b;b) < d(b;a))
Date html generated:
2020_05_20-PM-01_02_59
Last ObjectModification:
2019_12_11-PM-00_44_07
Theory : reals
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