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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.exponentiation.complex_power_of_complex_power
2theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
3instantiation6, 8  ⊢  
  :
4reference9  ⊢  
5instantiation7, 8, 9,  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.negation.complex_closure
7theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_left
8instantiation10, 11, 12, 13  ⊢  
  : , :
9instantiation64, 46, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.division.div_complex_closure
11instantiation15, 16, 17  ⊢  
  : , : , :
12instantiation64, 46, 18  ⊢  
  : , : , :
13instantiation19, 58  ⊢  
  :
14instantiation64, 52, 20  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
16instantiation37, 27, 21  ⊢  
  : , :
17instantiation22, 23, 24  ⊢  
  : , : , :
18instantiation64, 52, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
20instantiation64, 61, 26  ⊢  
  : , : , :
21instantiation37, 33, 34  ⊢  
  : , :
22axiom  ⊢  
 proveit.logic.equality.equals_transitivity
23instantiation28, 63, 66, 29, 32, 30, 27, 33, 34  ⊢  
  : , : , : , : , : , :
24instantiation28, 29, 66, 30, 31, 32, 38, 39, 33, 34  ⊢  
  : , : , : , : , : , :
25instantiation64, 61, 50  ⊢  
  : , : , :
26instantiation64, 35, 36  ⊢  
  : , : , :
27instantiation37, 38, 39  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.multiplication.disassociation
29axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
30theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31instantiation40  ⊢  
  : , :
32instantiation40  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34instantiation64, 46, 41  ⊢  
  : , : , :
35instantiation42, 43, 44  ⊢  
  : , :
36assumption  ⊢  
37theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
38instantiation64, 46, 45  ⊢  
  : , : , :
39instantiation64, 46, 47  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41instantiation64, 52, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
43theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
44instantiation49, 50, 51  ⊢  
  : , :
45instantiation64, 52, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation64, 54, 55  ⊢  
  : , : , :
48instantiation64, 61, 56  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation64, 57, 58  ⊢  
  : , : , :
51instantiation59, 60  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation64, 61, 62  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
56assumption  ⊢  
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
58theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
59theorem  ⊢  
 proveit.numbers.negation.int_closure
60instantiation64, 65, 63  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
62instantiation64, 65, 66  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
64theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements