Nuprl Lemma : r2-nontrivial
∃a:ℝ^2. (∃b:ℝ^2 [(d(a;a) < d(a;b))])
Proof
Definitions occuring in Statement :
real-vec-dist: d(x;y),
real-vec: ℝ^n,
rless: x < y,
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
sq_exists: ∃x:A [B[x]],
false: False,
prop: ℙ,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
decidable: Dec(P),
int_upper: {i...},
member: t ∈ T,
all: ∀x:A. B[x],
rless: x < y,
real-vec-sep: a ≠ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mexists{}a:\mBbbR{}\^{}2. (\mexists{}b:\mBbbR{}\^{}2 [(d(a;a) < d(a;b))])
Date html generated:
2020_05_20-PM-00_50_21
Last ObjectModification:
2020_01_09-PM-06_45_17
Theory : reals
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