1. 1
2. 2
3. 3
4. 4
5. 5
6. 6
7. 7
8. 8
9. 9
10. 10
11. 11
12. 12
13. 13
14. 14
15. 15
16. 16
17. 17
18. 18
19. 19
20. 20
21. 21
22. 22
23. 23
24. 24
25. 25
26. 26
27. 27
28. 28
29. 29
30. 30
31. 31
32. 32
33. 33
34. 34
35. 35
36. 36
37. 37
38. 38
39. 39
40. 40
41. 41
42. 42
43. 43
44. 44
45. 45

import data.real.basic

example (a b c : ℝ) : (c * b) * a = b * (a * c) :=
begin
  rw mul_comm c b,
  rw mul_assoc b c a,
  rw mul_comm c a
end

example (a b c : ℝ) : a * (b * c) = b * (a * c) :=
begin
  rw ←mul_assoc a b c,
  rw mul_comm a b,
  rw mul_assoc b a c
end

example (a b c : ℝ) : a * (b * c) = b * (c * a) :=
begin
  rw mul_comm,
  rw mul_assoc
end

example (a b c : ℝ) : a * (b * c) = b * (a * c) :=
begin
  rw ←mul_assoc,
  rw mul_comm a,
  rw mul_assoc
end

example (a b c d e f : ℝ) (h : b * c = e * f) :
  a * b * c * d = a * e * f * d :=
begin
  rw mul_assoc a,
  rw h,
  rw ←mul_assoc
end

example (a b c d : ℝ) (hyp : c = b * a - d) (hyp' : d = a * b) : c = 0 :=
begin
  rw hyp,
  rw hyp',
  rw mul_comm,
  rw sub_self
end