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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  ⊢  
  : , : , :
1reference26  ⊢  
2instantiation26, 3  ⊢  
  : , : , :
3instantiation4, 5, 6  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.equals_transitivity
5instantiation26, 7  ⊢  
  : , : , :
6instantiation8, 74, 71, 9, 10, 11, 43, 12, 13  ⊢  
  : , : , : , : , : , :
7instantiation14, 15, 16, 17  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.disassociation
9axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
10instantiation18  ⊢  
  : , :
11theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12instantiation19, 29, 20, 21  ⊢  
  : , :
13instantiation72, 50, 22  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
15instantiation26, 23  ⊢  
  : , : , :
16instantiation24, 25  ⊢  
  : , :
17instantiation26, 27  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19theorem  ⊢  
 proveit.numbers.division.div_complex_closure
20instantiation28, 43, 29  ⊢  
  : , :
21instantiation30, 37, 31  ⊢  
  : , : , :
22instantiation52, 53, 32  ⊢  
  : , : , :
23instantiation33, 34, 35  ⊢  
  : , :
24theorem  ⊢  
 proveit.logic.equality.equals_reversal
25instantiation36, 43, 45, 44, 37  ⊢  
  : , : , :
26axiom  ⊢  
 proveit.logic.equality.substitution
27instantiation38, 39, 40  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
29instantiation72, 50, 41  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
31instantiation42, 43  ⊢  
  :
32theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
33theorem  ⊢  
 proveit.numbers.addition.commutation
34instantiation72, 50, 44  ⊢  
  : , : , :
35instantiation72, 50, 45  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
37instantiation46, 70  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
39instantiation72, 47, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
41instantiation72, 58, 49  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43instantiation72, 50, 51  ⊢  
  : , : , :
44instantiation52, 53, 54  ⊢  
  : , : , :
45instantiation72, 58, 55  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
47theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
48instantiation72, 56, 57  ⊢  
  : , : , :
49instantiation72, 65, 68  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
51instantiation72, 58, 59  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
53instantiation60, 61  ⊢  
  : , :
54axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
55instantiation72, 65, 62  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
57instantiation72, 63, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
59instantiation72, 65, 66  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
62instantiation67, 68  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64instantiation72, 69, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
66instantiation72, 73, 71  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.negation.int_closure
68instantiation72, 73, 74  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
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