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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
0generalization1  ⊢  
1instantiation90, 18, 2,  ⊢  
  : , : , :
2instantiation3, 4, 5, 6,  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_real_closure
4instantiation90, 28, 7  ⊢  
  : , : , :
5instantiation8, 19, 92,  ⊢  
  : , :
6instantiation9, 10,  ⊢  
  :
7instantiation90, 35, 79  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
9theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
10instantiation11, 12, 13,  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
12instantiation14, 15, 16,  ⊢  
  :
13instantiation90, 18, 17  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
15instantiation90, 18, 19,  ⊢  
  : , : , :
16instantiation20, 21,  ⊢  
  : , :
17instantiation90, 28, 22  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
19instantiation23, 24, 25,  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
21instantiation26, 27,  ⊢  
  : , :
22instantiation90, 35, 89  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
24instantiation90, 28, 29,  ⊢  
  : , : , :
25instantiation30, 31  ⊢  
  :
26theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
27instantiation32, 33, 43, 34,  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
29instantiation90, 35, 43,  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.negation.real_closure
31instantiation36, 37, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
33instantiation39, 40, 82, 41  ⊢  
  : , : , : , : , :
34instantiation42, 43, 44, 45,  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
37instantiation46, 47, 48  ⊢  
  : , : , :
38instantiation49, 50  ⊢  
  :
39theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
40axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
41theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
43instantiation90, 51, 60,  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
45instantiation52, 53, 54,  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
47instantiation55, 56  ⊢  
  : , :
48theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
49theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
50theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
51instantiation77, 58, 59  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
53instantiation57, 58, 59, 60,  ⊢  
  : , : , :
54instantiation61, 62  ⊢  
  :
55theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
57theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
58instantiation83, 63, 79  ⊢  
  : , :
59instantiation88, 64  ⊢  
  :
60assumption  ⊢  
61theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
62instantiation65, 66  ⊢  
  :
63instantiation88, 84  ⊢  
  :
64instantiation83, 71, 79  ⊢  
  : , :
65theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
66instantiation67, 68, 69  ⊢  
  : , :
67theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
68instantiation70, 71, 72  ⊢  
  :
69theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
70theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
71instantiation90, 73, 81  ⊢  
  : , : , :
72instantiation74, 75, 76  ⊢  
  : , : , :
73instantiation77, 79, 80  ⊢  
  : , :
74theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
75theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
76instantiation78, 79, 80, 81  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
78theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
79instantiation90, 91, 82  ⊢  
  : , : , :
80instantiation83, 84, 85  ⊢  
  : , :
81assumption  ⊢  
82theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
83theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
84instantiation90, 86, 87  ⊢  
  : , : , :
85instantiation88, 89  ⊢  
  :
86theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
87theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
88theorem  ⊢  
 proveit.numbers.negation.int_closure
89instantiation90, 91, 92  ⊢  
  : , : , :
90theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
91theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
92theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2