Step
*
of Lemma
r2-plane-separation
No Annotations
∀a,b:ℝ^2. ∀u:{u:ℝ^2| r2-left(u;a;b)} . ∀v:{v:ℝ^2| r2-left(v;b;a)} .
(∃x:ℝ^2 [((¬(r2-left(a;b;x) ∨ r2-left(a;x;b)))
∧ ((¬(d(u;v) < d(u;x))) ∧ (¬(d(u;v) < d(x;v))))
∧ (¬(r2-left(u;x;v) ∨ r2-left(u;v;x))))])
BY
{ (InstLemma `r2-plane-separation1` [] THEN RepeatFor 5 (ParallelLast')) }
1
.....set predicate.....
1. a : ℝ^2
2. b : ℝ^2
3. u : {u:ℝ^2| r2-left(u;a;b)}
4. v : {v:ℝ^2| r2-left(v;b;a)}
5. x : ℝ^2
6. (¬((¬a_b_x) ∧ (¬b_x_a) ∧ (¬x_a_b))) ∧ u_x_v
⊢ (¬(r2-left(a;b;x) ∨ r2-left(a;x;b)))
∧ ((¬(d(u;v) < d(u;x))) ∧ (¬(d(u;v) < d(x;v))))
∧ (¬(r2-left(u;x;v) ∨ r2-left(u;v;x)))
Latex:
Latex:
No Annotations
\mforall{}a,b:\mBbbR{}\^{}2. \mforall{}u:\{u:\mBbbR{}\^{}2| r2-left(u;a;b)\} . \mforall{}v:\{v:\mBbbR{}\^{}2| r2-left(v;b;a)\} .
(\mexists{}x:\mBbbR{}\^{}2 [((\mneg{}(r2-left(a;b;x) \mvee{} r2-left(a;x;b)))
\mwedge{} ((\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))))])
By
Latex:
(InstLemma `r2-plane-separation1` [] THEN RepeatFor 5 (ParallelLast'))
Home
Index