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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,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
2instantiation75, 4, 5,  ⊢  
  : , : , :
3instantiation6, 7,  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
5instantiation8, 9, 10,  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
7instantiation11, 12,  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
9instantiation75, 13, 14,  ⊢  
  : , : , :
10instantiation15, 16  ⊢  
  :
11theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
12instantiation17, 18, 28, 19,  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
14instantiation75, 20, 28,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.negation.real_closure
16instantiation21, 22, 23  ⊢  
  : , :
17theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
18instantiation24, 25, 67, 26  ⊢  
  : , : , : , : , :
19instantiation27, 28, 29, 30,  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
21theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
22instantiation31, 32, 33  ⊢  
  : , : , :
23instantiation34, 35  ⊢  
  :
24theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
28instantiation75, 36, 45,  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
30instantiation37, 38, 39,  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation40, 41  ⊢  
  : , :
33theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
34theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
35theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
36instantiation62, 43, 44  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
38instantiation42, 43, 44, 45,  ⊢  
  : , : , :
39instantiation46, 47  ⊢  
  :
40theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
43instantiation68, 48, 64  ⊢  
  : , :
44instantiation73, 49  ⊢  
  :
45assumption  ⊢  
46theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
47instantiation50, 51  ⊢  
  :
48instantiation73, 69  ⊢  
  :
49instantiation68, 56, 64  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
51instantiation52, 53, 54  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
53instantiation55, 56, 57  ⊢  
  :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
55theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
56instantiation75, 58, 66  ⊢  
  : , : , :
57instantiation59, 60, 61  ⊢  
  : , : , :
58instantiation62, 64, 65  ⊢  
  : , :
59theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
60theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
61instantiation63, 64, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
63theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
64instantiation75, 76, 67  ⊢  
  : , : , :
65instantiation68, 69, 70  ⊢  
  : , :
66assumption  ⊢  
67theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
68theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
69instantiation75, 71, 72  ⊢  
  : , : , :
70instantiation73, 74  ⊢  
  :
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
72theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
73theorem  ⊢  
 proveit.numbers.negation.int_closure
74instantiation75, 76, 77  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2