Nuprl Lemma : r2-sep-or
∀a:ℝ^2. ∀b:{b:ℝ^2| d(a;a) < d(a;b)} . ∀c:ℝ^2. ((d(a;a) < d(a;c)) ∨ (d(b;b) < d(b;c)))
Proof
Definitions occuring in Statement :
real-vec-dist: d(x;y),
real-vec: ℝ^n,
rless: x < y,
all: ∀x:A. B[x],
or: P ∨ Q,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
real-vec-sep: a ≠ b,
or: P ∨ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}a:\mBbbR{}\^{}2. \mforall{}b:\{b:\mBbbR{}\^{}2| d(a;a) < d(a;b)\} . \mforall{}c:\mBbbR{}\^{}2. ((d(a;a) < d(a;c)) \mvee{} (d(b;b) < d(b;c)))
Date html generated:
2020_05_20-PM-00_44_32
Last ObjectModification:
2019_12_11-AM-11_21_32
Theory : reals
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