Step
*
1
2
2
1
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. q : ℝ^2
6. b-a-q
7. (d(c;d) + d(c;b)) < d(b;q)
8. q_a_b
9. d(b;q) ≤ (d(b;c) + d(c;q))
10. (d(c;d) + d(c;b)) < (d(b;c) + d(c;q))
⊢ d(c;d) < d(c;q)
BY
{ ((Assert d(c;b) = d(b;c) BY Auto) THEN RWO "-1" (-2) THEN Auto) }
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. q : \mBbbR{}\^{}2
6. b-a-q
7. (d(c;d) + d(c;b)) < d(b;q)
8. q\_a\_b
9. d(b;q) \mleq{} (d(b;c) + d(c;q))
10. (d(c;d) + d(c;b)) < (d(b;c) + d(c;q))
\mvdash{} d(c;d) < d(c;q)
By
Latex:
((Assert d(c;b) = d(b;c) BY Auto) THEN RWO "-1" (-2) THEN Auto)
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