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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  ⊢  
  : , : , :
1reference4  ⊢  
2instantiation4, 5, 6  ⊢  
  : , : , :
3instantiation7, 8, 9  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.equals_transitivity
5instantiation32, 15  ⊢  
  : , : , :
6instantiation32, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_basic
8instantiation11, 12, 13  ⊢  
  : , :
9instantiation14  ⊢  
  :
10instantiation32, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
12instantiation16, 25, 17, 18  ⊢  
  : , :
13instantiation77, 51, 19  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
15instantiation20, 21, 22, 23  ⊢  
  : , : , : , :
16theorem  ⊢  
 proveit.numbers.division.div_complex_closure
17instantiation24, 41, 25  ⊢  
  : , :
18instantiation26, 42, 27  ⊢  
  : , : , :
19instantiation77, 61, 28  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
21instantiation32, 29  ⊢  
  : , : , :
22instantiation30, 31  ⊢  
  : , :
23instantiation32, 33  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
25instantiation77, 51, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
27instantiation35, 41  ⊢  
  :
28instantiation77, 68, 36  ⊢  
  : , : , :
29instantiation37, 38, 39  ⊢  
  : , :
30theorem  ⊢  
 proveit.logic.equality.equals_reversal
31instantiation40, 41, 50, 49, 42  ⊢  
  : , : , :
32axiom  ⊢  
 proveit.logic.equality.substitution
33instantiation43, 44, 45  ⊢  
  : , :
34instantiation77, 61, 46  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
36instantiation47, 69, 48  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.addition.commutation
38instantiation77, 51, 49  ⊢  
  : , : , :
39instantiation77, 51, 50  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
41instantiation77, 51, 52  ⊢  
  : , : , :
42instantiation53, 76  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
44instantiation77, 54, 55  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
46instantiation77, 68, 73  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
48instantiation77, 56, 59  ⊢  
  : , : , :
49instantiation57, 58, 59  ⊢  
  : , : , :
50instantiation77, 61, 60  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52instantiation77, 61, 62  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
55instantiation77, 63, 64  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
57theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
58instantiation65, 66  ⊢  
  : , :
59axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
60instantiation77, 68, 67  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
62instantiation77, 68, 69  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
64instantiation77, 70, 71  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
67instantiation72, 73  ⊢  
  :
68theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
69instantiation77, 78, 74  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
71instantiation77, 75, 76  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.negation.int_closure
73instantiation77, 78, 79  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
77theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
79theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1