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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  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
2instantiation70, 46, 4  ⊢  
  : , : , :
3instantiation5, 6, 7  ⊢  
  : , : , :
4instantiation70, 36, 8  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
6instantiation13, 14, 9  ⊢  
  : , :
7instantiation10, 11, 12  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
9instantiation13, 22, 23  ⊢  
  : , :
10axiom  ⊢  
 proveit.logic.equality.equals_transitivity
11instantiation15, 69, 49, 16, 19, 17, 14, 22, 23  ⊢  
  : , : , : , : , : , :
12instantiation15, 16, 49, 17, 18, 19, 20, 21, 22, 23  ⊢  
  : , : , : , : , : , :
13theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
14instantiation70, 46, 24  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.disassociation
16axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
17theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18instantiation25  ⊢  
  : , :
19instantiation25  ⊢  
  : , :
20instantiation70, 46, 30  ⊢  
  : , : , :
21instantiation70, 46, 31  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
23instantiation26, 27, 28  ⊢  
  : , :
24instantiation29, 30, 31  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
27instantiation70, 46, 32  ⊢  
  : , : , :
28instantiation33, 34  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
30instantiation70, 50, 35  ⊢  
  : , : , :
31instantiation70, 36, 37  ⊢  
  : , : , :
32instantiation38, 39  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.negation.complex_closure
34instantiation40, 41, 42, 43  ⊢  
  : , :
35instantiation70, 55, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
39theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
40theorem  ⊢  
 proveit.numbers.division.div_complex_closure
41instantiation70, 46, 45  ⊢  
  : , : , :
42instantiation70, 46, 47  ⊢  
  : , : , :
43instantiation48, 54  ⊢  
  :
44instantiation70, 68, 49  ⊢  
  : , : , :
45instantiation70, 50, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation52, 53, 54  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation70, 55, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
53instantiation57, 58  ⊢  
  : , :
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation70, 59, 60  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
59instantiation61, 62, 67  ⊢  
  : , :
60assumption  ⊢  
61theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
62instantiation63, 64, 65  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
64instantiation66, 67  ⊢  
  :
65instantiation70, 68, 69  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.negation.int_closure
67instantiation70, 71, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
70theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
72theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos