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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
0modus ponens1, 2  ⊢  
1instantiation3  ⊢  
  : , : , :
2generalization4  ⊢  
3theorem  ⊢  
 proveit.numbers.summation.summation_complex_closure
4instantiation86, 21, 5,  ⊢  
  : , : , :
5instantiation6, 7, 8, 9,  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.division.div_real_closure
7instantiation86, 31, 10  ⊢  
  : , : , :
8instantiation11, 22, 88,  ⊢  
  : , :
9instantiation12, 13,  ⊢  
  :
10instantiation86, 38, 75  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
13instantiation14, 15, 16,  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
15instantiation17, 18, 19,  ⊢  
  :
16instantiation86, 21, 20  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
18instantiation86, 21, 22,  ⊢  
  : , : , :
19instantiation23, 24,  ⊢  
  : , :
20instantiation86, 31, 25  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
22instantiation26, 27, 28,  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
24instantiation29, 30,  ⊢  
  : , :
25instantiation86, 38, 85  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
27instantiation86, 31, 32,  ⊢  
  : , : , :
28instantiation33, 34  ⊢  
  :
29theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
30instantiation35, 36, 52, 37,  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
32instantiation86, 38, 52,  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.negation.real_closure
34instantiation39, 40, 41  ⊢  
  : , :
35theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
36instantiation42, 43, 78, 44  ⊢  
  : , : , : , : , :
37instantiation45, 46,  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
39theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
40instantiation47, 48, 49  ⊢  
  : , : , :
41instantiation50, 51  ⊢  
  :
42theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
43axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
44theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
46instantiation66, 52, 53,  ⊢  
  :
47theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
48instantiation54, 55  ⊢  
  : , :
49theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
50theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
51theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
52instantiation86, 56, 62,  ⊢  
  : , : , :
53instantiation70, 57, 58,  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
56instantiation73, 61, 80  ⊢  
  : , :
57instantiation59, 60  ⊢  
  :
58instantiation74, 61, 80, 62,  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
60instantiation63, 64, 65  ⊢  
  : , :
61instantiation79, 67, 75  ⊢  
  : , :
62assumption  ⊢  
63theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
64instantiation66, 67, 68  ⊢  
  :
65theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
66theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
67instantiation86, 69, 77  ⊢  
  : , : , :
68instantiation70, 71, 72  ⊢  
  : , : , :
69instantiation73, 75, 76  ⊢  
  : , :
70theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
71theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
72instantiation74, 75, 76, 77  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
74theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
75instantiation86, 87, 78  ⊢  
  : , : , :
76instantiation79, 80, 81  ⊢  
  : , :
77assumption  ⊢  
78theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
79theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
80instantiation86, 82, 83  ⊢  
  : , : , :
81instantiation84, 85  ⊢  
  :
82theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
83theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
84theorem  ⊢  
 proveit.numbers.negation.int_closure
85instantiation86, 87, 88  ⊢  
  : , : , :
86theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
88theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2