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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, 4, 5*,  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
2reference12  ⊢  
3instantiation90, 6, 7  ⊢  
  : , : , :
4instantiation8, 9, 10,  ⊢  
  : , :
5instantiation11, 12  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
7instantiation90, 13, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
9instantiation15, 16, 17,  ⊢  
  :
10instantiation90, 22, 18  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
12instantiation90, 22, 19  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
14instantiation90, 20, 21  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
16instantiation90, 22, 23,  ⊢  
  : , : , :
17instantiation24, 25,  ⊢  
  : , :
18instantiation90, 35, 26  ⊢  
  : , : , :
19instantiation90, 35, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
21instantiation90, 28, 29  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
23instantiation30, 31, 32,  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
25instantiation33, 34,  ⊢  
  : , :
26instantiation90, 42, 89  ⊢  
  : , : , :
27instantiation90, 42, 79  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
29theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
30theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
31instantiation90, 35, 36,  ⊢  
  : , : , :
32instantiation37, 38  ⊢  
  :
33theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
34instantiation39, 40, 56, 41,  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation90, 42, 56,  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.negation.real_closure
38instantiation43, 44, 45  ⊢  
  : , :
39theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
40instantiation46, 47, 82, 48  ⊢  
  : , : , : , : , :
41instantiation49, 50,  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
44instantiation51, 52, 53  ⊢  
  : , : , :
45instantiation54, 55  ⊢  
  :
46theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
47axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
48theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
50instantiation70, 56, 57,  ⊢  
  :
51theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
52instantiation58, 59  ⊢  
  : , :
53theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
54theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
55theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
56instantiation90, 60, 66,  ⊢  
  : , : , :
57instantiation74, 61, 62,  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60instantiation77, 65, 84  ⊢  
  : , :
61instantiation63, 64  ⊢  
  :
62instantiation78, 65, 84, 66,  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
64instantiation67, 68, 69  ⊢  
  : , :
65instantiation83, 71, 79  ⊢  
  : , :
66assumption  ⊢  
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
*equality replacement requirements