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Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3, 4  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
2instantiation21, 5, 6  ⊢  
  : , : , :
3instantiation7  ⊢  
  :
4instantiation8, 14  ⊢  
  : , :
5instantiation21, 9, 10  ⊢  
  : , : , :
6instantiation11, 12  ⊢  
  :
7axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
8theorem  ⊢  
 proveit.logic.equality.equals_reversal
9instantiation25, 13  ⊢  
  : , : , :
10instantiation25, 14  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
12instantiation67, 53, 15  ⊢  
  : , : , :
13instantiation16, 29  ⊢  
  :
14instantiation17, 28, 43, 48, 18*  ⊢  
  : , :
15instantiation19, 20, 35  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_right
17theorem  ⊢  
 proveit.numbers.division.div_as_mult
18instantiation21, 22, 23  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
20instantiation67, 59, 24  ⊢  
  : , : , :
21axiom  ⊢  
 proveit.logic.equality.equals_transitivity
22instantiation25, 26  ⊢  
  : , : , :
23instantiation27, 28, 29  ⊢  
  : , :
24instantiation67, 30, 31  ⊢  
  : , : , :
25axiom  ⊢  
 proveit.logic.equality.substitution
26instantiation32, 33, 49, 34*  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.multiplication.commutation
28instantiation67, 53, 35  ⊢  
  : , : , :
29instantiation67, 53, 36  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
31instantiation37, 38, 39  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
33instantiation67, 40, 41  ⊢  
  : , : , :
34instantiation42, 43  ⊢  
  :
35instantiation67, 44, 45  ⊢  
  : , : , :
36instantiation46, 47, 54, 48  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
38instantiation67, 50, 49  ⊢  
  : , : , :
39instantiation67, 50, 63  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
41instantiation67, 51, 52  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43instantiation67, 53, 54  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
46theorem  ⊢  
 proveit.numbers.division.div_real_closure
47instantiation67, 59, 55  ⊢  
  : , : , :
48instantiation56, 63  ⊢  
  :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
52instantiation67, 57, 58  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
54instantiation67, 59, 60  ⊢  
  : , : , :
55instantiation67, 64, 61  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
58instantiation67, 62, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
60instantiation67, 64, 65  ⊢  
  : , : , :
61instantiation67, 68, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
64theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
65instantiation67, 68, 69  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
67theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements