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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,  ⊢  
  :
5instantiation82, 10, 9  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
7instantiation82, 10, 11,  ⊢  
  : , : , :
8instantiation12, 13,  ⊢  
  : , :
9instantiation82, 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,  ⊢  
  : , :
14instantiation82, 27, 81  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
16instantiation82, 20, 21,  ⊢  
  : , : , :
17instantiation22, 23  ⊢  
  :
18theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
19instantiation24, 25, 35, 26,  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
21instantiation82, 27, 35,  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.negation.real_closure
23instantiation28, 29, 30  ⊢  
  : , :
24theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
25instantiation31, 32, 74, 33  ⊢  
  : , : , : , : , :
26instantiation34, 35, 36, 37,  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
28theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
29instantiation38, 39, 40  ⊢  
  : , : , :
30instantiation41, 42  ⊢  
  :
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.ordering.less_is_not_eq_int
35instantiation82, 43, 52,  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
37instantiation44, 45, 46,  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
39instantiation47, 48  ⊢  
  : , :
40theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
41theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
42theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
43instantiation69, 50, 51  ⊢  
  : , :
44theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
45instantiation49, 50, 51, 52,  ⊢  
  : , : , :
46instantiation53, 54  ⊢  
  :
47theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
49theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
50instantiation75, 55, 71  ⊢  
  : , :
51instantiation80, 56  ⊢  
  :
52assumption  ⊢  
53theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
54instantiation57, 58  ⊢  
  :
55instantiation80, 76  ⊢  
  :
56instantiation75, 63, 71  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
58instantiation59, 60, 61  ⊢  
  : , :
59theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
60instantiation62, 63, 64  ⊢  
  :
61theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
62theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
63instantiation82, 65, 73  ⊢  
  : , : , :
64instantiation66, 67, 68  ⊢  
  : , : , :
65instantiation69, 71, 72  ⊢  
  : , :
66theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
67theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
68instantiation70, 71, 72, 73  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
70theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
71instantiation82, 83, 74  ⊢  
  : , : , :
72instantiation75, 76, 77  ⊢  
  : , :
73assumption  ⊢  
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
75theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
76instantiation82, 78, 79  ⊢  
  : , : , :
77instantiation80, 81  ⊢  
  :
78theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
79theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
80theorem  ⊢  
 proveit.numbers.negation.int_closure
81instantiation82, 83, 84  ⊢  
  : , : , :
82theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
83theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
84theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2