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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  ⊢  
  : , :
9instantiation67, 42, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.division.div_complex_closure
11instantiation15, 16, 17  ⊢  
  : , : , :
12instantiation67, 42, 18  ⊢  
  : , : , :
13instantiation19, 64  ⊢  
  :
14instantiation67, 45, 20  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
16instantiation36, 27, 21  ⊢  
  : , :
17instantiation22, 23, 24  ⊢  
  : , : , :
18instantiation67, 45, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
20instantiation67, 50, 26  ⊢  
  : , : , :
21instantiation36, 33, 34  ⊢  
  : , :
22axiom  ⊢  
 proveit.logic.equality.equals_transitivity
23instantiation28, 69, 54, 29, 32, 30, 27, 33, 34  ⊢  
  : , : , : , : , : , :
24instantiation28, 29, 54, 30, 31, 32, 37, 38, 33, 34  ⊢  
  : , : , : , : , : , :
25instantiation67, 50, 61  ⊢  
  : , : , :
26instantiation67, 52, 35  ⊢  
  : , : , :
27instantiation36, 37, 38  ⊢  
  : , :
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
31instantiation39  ⊢  
  : , :
32instantiation39  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34instantiation67, 42, 40  ⊢  
  : , : , :
35assumption  ⊢  
36theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
37instantiation67, 42, 41  ⊢  
  : , : , :
38instantiation67, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40instantiation67, 45, 44  ⊢  
  : , : , :
41instantiation67, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation67, 47, 48  ⊢  
  : , : , :
44instantiation67, 50, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation67, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49instantiation67, 52, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation67, 68, 54  ⊢  
  : , : , :
52instantiation55, 56, 57  ⊢  
  : , :
53instantiation58, 59, 64  ⊢  
  : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
55theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
56theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
57instantiation60, 61, 62  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.modular.mod_natpos_in_interval
59assumption  ⊢  
60theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
61instantiation67, 63, 64  ⊢  
  : , : , :
62instantiation65, 66  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
64theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
65theorem  ⊢  
 proveit.numbers.negation.int_closure
66instantiation67, 68, 69  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements