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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  ⊢  
  : , : , :
1reference52  ⊢  
2instantiation60, 4  ⊢  
  : , : , :
3instantiation52, 5, 6  ⊢  
  : , : , :
4instantiation60, 7  ⊢  
  : , : , :
5instantiation52, 8, 9  ⊢  
  : , : , :
6instantiation68, 16  ⊢  
  :
7instantiation10, 69  ⊢  
  :
8instantiation11, 12, 80, 73, 13, 14, 69, 15, 16  ⊢  
  : , : , : , : , : , :
9instantiation60, 17  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
11theorem  ⊢  
 proveit.numbers.multiplication.association
12axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
13theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14instantiation18  ⊢  
  : , :
15instantiation19, 48, 69, 20  ⊢  
  : , :
16instantiation78, 71, 21  ⊢  
  : , : , :
17instantiation28, 22, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19theorem  ⊢  
 proveit.numbers.division.div_complex_closure
20instantiation24, 65  ⊢  
  :
21instantiation25, 26, 27  ⊢  
  : , : , :
22instantiation28, 29, 30  ⊢  
  : , : , :
23instantiation31, 32, 33, 34  ⊢  
  : , : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
26instantiation35, 36  ⊢  
  : , :
27theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
28theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
29instantiation37, 48, 38, 39  ⊢  
  : , : , : , : , :
30instantiation52, 40, 41  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
32instantiation60, 42  ⊢  
  : , : , :
33instantiation60, 42  ⊢  
  : , : , :
34instantiation63, 48  ⊢  
  :
35theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
37theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
38instantiation78, 44, 43  ⊢  
  : , : , :
39instantiation78, 44, 45  ⊢  
  : , : , :
40instantiation60, 46  ⊢  
  : , : , :
41instantiation60, 47  ⊢  
  : , : , :
42instantiation62, 48  ⊢  
  :
43instantiation78, 50, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
45instantiation78, 50, 51  ⊢  
  : , : , :
46instantiation52, 53, 54  ⊢  
  : , : , :
47instantiation60, 55  ⊢  
  : , : , :
48instantiation78, 71, 56  ⊢  
  : , : , :
49instantiation78, 58, 57  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
51instantiation78, 58, 59  ⊢  
  : , : , :
52axiom  ⊢  
 proveit.logic.equality.equals_transitivity
53instantiation60, 61  ⊢  
  : , : , :
54instantiation62, 69  ⊢  
  :
55instantiation63, 69  ⊢  
  :
56instantiation78, 74, 64  ⊢  
  : , : , :
57instantiation78, 66, 65  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
59instantiation78, 66, 67  ⊢  
  : , : , :
60axiom  ⊢  
 proveit.logic.equality.substitution
61instantiation68, 69  ⊢  
  :
62theorem  ⊢  
 proveit.numbers.division.frac_one_denom
63theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
64instantiation78, 76, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
67theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
68theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
69instantiation78, 71, 72  ⊢  
  : , : , :
70instantiation78, 79, 73  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
72instantiation78, 74, 75  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
74theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
75instantiation78, 76, 77  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
77instantiation78, 79, 80  ⊢  
  : , : , :
78theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
80theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2