Step
*
1
2
of Lemma
r2-straightedge-compass
1. c : ℝ^2
2. d : ℝ^2
3. a : ℝ^2
4. b : {b:ℝ^2| b ≠ a ∧ c_b_d}
5. ∀x:ℝ. ∃q:ℝ^2. (b-a-q ∧ (x < d(b;q)))
⊢ ∃q:ℝ^2. (q_a_b ∧ (d(c;d) < d(c;q)))
BY
{ ((D -1 With ⌜d(c;d) + d(c;b)⌝ THENA Auto) THEN ParallelLast THEN Auto) }
1
1. c : ℝ^2
2. d : ℝ^2
3. a : ℝ^2
4. b : {b:ℝ^2| b ≠ a ∧ c_b_d}
5. q : ℝ^2
6. b-a-q
7. (d(c;d) + d(c;b)) < d(b;q)
⊢ q_a_b
2
1. c : ℝ^2
2. d : ℝ^2
3. a : ℝ^2
4. b : {b:ℝ^2| b ≠ a ∧ c_b_d}
5. q : ℝ^2
6. b-a-q
7. (d(c;d) + d(c;b)) < d(b;q)
8. q_a_b
⊢ d(c;d) < d(c;q)
Latex:
Latex:
1. c : \mBbbR{}\^{}2
2. d : \mBbbR{}\^{}2
3. a : \mBbbR{}\^{}2
4. b : \{b:\mBbbR{}\^{}2| b \mneq{} a \mwedge{} c\_b\_d\}
5. \mforall{}x:\mBbbR{}. \mexists{}q:\mBbbR{}\^{}2. (b-a-q \mwedge{} (x < d(b;q)))
\mvdash{} \mexists{}q:\mBbbR{}\^{}2. (q\_a\_b \mwedge{} (d(c;d) < d(c;q)))
By
Latex:
((D -1 With \mkleeneopen{}d(c;d) + d(c;b)\mkleeneclose{} THENA Auto) THEN ParallelLast THEN Auto)
Home
Index