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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,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
2instantiation3, 4, 5,  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
4instantiation6, 7, 8,  ⊢  
  :
5instantiation75, 10, 9  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
7instantiation75, 10, 11,  ⊢  
  : , : , :
8instantiation12, 13,  ⊢  
  : , :
9instantiation75, 20, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
11instantiation15, 16, 17,  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
13instantiation18, 19,  ⊢  
  : , :
14instantiation75, 27, 74  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
16instantiation75, 20, 21,  ⊢  
  : , : , :
17instantiation22, 23  ⊢  
  :
18theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
19instantiation24, 25, 41, 26,  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
21instantiation75, 27, 41,  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.negation.real_closure
23instantiation28, 29, 30  ⊢  
  : , :
24theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
25instantiation31, 32, 67, 33  ⊢  
  : , : , : , : , :
26instantiation34, 35,  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
28theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
29instantiation36, 37, 38  ⊢  
  : , : , :
30instantiation39, 40  ⊢  
  :
31theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
32axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
33theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
35instantiation55, 41, 42,  ⊢  
  :
36theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
37instantiation43, 44  ⊢  
  : , :
38theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
39theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
40theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
41instantiation75, 45, 51,  ⊢  
  : , : , :
42instantiation59, 46, 47,  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
45instantiation62, 50, 69  ⊢  
  : , :
46instantiation48, 49  ⊢  
  :
47instantiation63, 50, 69, 51,  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
49instantiation52, 53, 54  ⊢  
  : , :
50instantiation68, 56, 64  ⊢  
  : , :
51assumption  ⊢  
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