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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  ⊢  
  : , : , :
1reference5  ⊢  
2instantiation36, 4  ⊢  
  : , : , :
3instantiation5, 6, 7  ⊢  
  : , : , :
4instantiation36, 8  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation9, 94, 10, 14, 11, 15, 21, 17, 57, 12  ⊢  
  : , : , : , : , : , :
7instantiation13, 14, 97, 15, 16, 21, 17, 57, 18  ⊢  
  : , : , : , : , : , : , : , :
8instantiation36, 19  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.addition.disassociation
10theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
11instantiation20  ⊢  
  : , : , :
12instantiation56, 21  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
14axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
15theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16instantiation22  ⊢  
  : , :
17instantiation56, 23  ⊢  
  :
18instantiation24  ⊢  
  :
19instantiation25, 26, 27, 28  ⊢  
  : , : , : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
21instantiation95, 74, 29  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23instantiation30, 31, 32  ⊢  
  : , :
24axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
25theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
26instantiation36, 33  ⊢  
  : , : , :
27instantiation34, 35  ⊢  
  : , :
28instantiation36, 37  ⊢  
  : , : , :
29instantiation95, 84, 38  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
31instantiation39, 57, 40, 41  ⊢  
  : , :
32instantiation51, 65, 43  ⊢  
  : , :
33instantiation42, 43, 44  ⊢  
  : , :
34theorem  ⊢  
 proveit.logic.equality.equals_reversal
35instantiation45, 65, 46, 55, 53  ⊢  
  : , : , :
36axiom  ⊢  
 proveit.logic.equality.substitution
37instantiation47, 48, 49  ⊢  
  : , :
38instantiation95, 92, 50  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.division.div_complex_closure
40instantiation51, 65, 57  ⊢  
  : , :
41instantiation52, 53, 54  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.addition.commutation
43instantiation95, 74, 55  ⊢  
  : , : , :
44instantiation56, 57  ⊢  
  :
45theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
46instantiation58, 69  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
48instantiation95, 59, 60  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
50instantiation95, 61, 62  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
52theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
53instantiation63, 88  ⊢  
  :
54instantiation64, 65  ⊢  
  :
55instantiation66, 67, 68  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.negation.complex_closure
57instantiation95, 74, 69  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.negation.real_closure
59theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
60instantiation95, 70, 71  ⊢  
  : , : , :
61instantiation72, 86, 73  ⊢  
  : , :
62assumption  ⊢  
63theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
64theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
65instantiation95, 74, 75  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
67instantiation76, 77  ⊢  
  : , :
68axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
69instantiation95, 84, 78  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
71instantiation95, 79, 80  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
73instantiation81, 82, 83  ⊢  
  : , :
74theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
75instantiation95, 84, 85  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
78instantiation95, 92, 86  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
80instantiation95, 87, 88  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
82instantiation95, 89, 90  ⊢  
  : , : , :
83instantiation91, 93  ⊢  
  :
84theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
85instantiation95, 92, 93  ⊢  
  : , : , :
86instantiation95, 96, 94  ⊢  
  : , : , :
87theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
88theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
89theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
90theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
91theorem  ⊢  
 proveit.numbers.negation.int_closure
92theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
93instantiation95, 96, 97  ⊢  
  : , : , :
94theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
95theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
96theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
97theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2