Nuprl Lemma : r2-gt-or
∀a,b,c:ℝ^2. ∀d:{d:ℝ^2| d(c;d) < d(a;b)} . ∀x,y:ℝ^2. ((d(c;d) < d(x;y)) ∨ (d(x;y) < d(a;b)))
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
Latex:
\mforall{}a,b,c:\mBbbR{}\^{}2. \mforall{}d:\{d:\mBbbR{}\^{}2| d(c;d) < d(a;b)\} . \mforall{}x,y:\mBbbR{}\^{}2. ((d(c;d) < d(x;y)) \mvee{} (d(x;y) < d(a;b)))
Date html generated:
2020_05_20-PM-01_10_29
Last ObjectModification:
2020_01_28-AM-10_59_48
Theory : reals!model!euclidean!geometry
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