Nuprl Lemma : r2-be-iff
∀u,v,x:ℝ^2. (u_x_v ⇐⇒ ((¬(d(u;v) < d(u;x))) ∧ (¬(d(u;v) < d(x;v)))) ∧ (¬(r2-left(u;x;v) ∨ r2-left(u;v;x))))
Proof
Definitions occuring in Statement :
r2-left: r2-left(p;q;r),
rv-be: a_b_c,
real-vec-dist: d(x;y),
real-vec: ℝ^n,
rless: x < y,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
uiff: uiff(P;Q),
req_int_terms: t1 ≡ t2,
top: Top,
cand: A c∧ B,
stable: Stable{P},
rv-be: a_b_c,
real-vec-sep: a ≠ b
Latex:
\mforall{}u,v,x:\mBbbR{}\^{}2.
(u\_x\_v \mLeftarrow{}{}\mRightarrow{} ((\mneg{}(d(u;v) < d(u;x))) \mwedge{} (\mneg{}(d(u;v) < d(x;v)))) \mwedge{} (\mneg{}(r2-left(u;x;v) \mvee{} r2-left(u;v;x))))
Date html generated:
2020_05_20-PM-01_02_31
Last ObjectModification:
2019_12_11-PM-00_19_03
Theory : reals
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