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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
5instantiation31, 15  ⊢  
  : , : , :
6instantiation31, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_basic
8instantiation11, 12, 13  ⊢  
  : , :
9instantiation14  ⊢  
  :
10instantiation31, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
12instantiation16, 46, 17, 18  ⊢  
  : , :
13instantiation72, 55, 19  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
15instantiation20, 21, 22, 23  ⊢  
  : , : , : , :
16theorem  ⊢  
 proveit.numbers.division.div_complex_closure
17instantiation24, 38, 46  ⊢  
  : , :
18instantiation25, 40, 26  ⊢  
  : , : , :
19instantiation52, 53, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
21instantiation31, 28  ⊢  
  : , : , :
22instantiation29, 30  ⊢  
  : , :
23instantiation31, 32  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
25theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
26instantiation33, 38  ⊢  
  :
27theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
28instantiation34, 35, 36  ⊢  
  : , :
29theorem  ⊢  
 proveit.logic.equality.equals_reversal
30instantiation37, 38, 39, 44, 40  ⊢  
  : , : , :
31axiom  ⊢  
 proveit.logic.equality.substitution
32instantiation41, 42, 43  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
34theorem  ⊢  
 proveit.numbers.addition.commutation
35instantiation72, 55, 44  ⊢  
  : , : , :
36instantiation45, 46  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
38instantiation72, 55, 47  ⊢  
  : , : , :
39instantiation48, 56  ⊢  
  :
40instantiation49, 71  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
42instantiation72, 50, 51  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
44instantiation52, 53, 54  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.negation.complex_closure
46instantiation72, 55, 56  ⊢  
  : , : , :
47instantiation72, 62, 57  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.negation.real_closure
49theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
51instantiation72, 58, 59  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
53instantiation60, 61  ⊢  
  : , :
54axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
55theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
56instantiation72, 62, 63  ⊢  
  : , : , :
57instantiation72, 67, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
59instantiation72, 65, 66  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
62theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
63instantiation72, 67, 68  ⊢  
  : , : , :
64instantiation72, 73, 69  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
66instantiation72, 70, 71  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
68instantiation72, 73, 74  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1