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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
2instantiation61, 36, 4  ⊢  
  : , : , :
3instantiation5, 6  ⊢  
  :
4instantiation61, 41, 7  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.negation.complex_closure
6instantiation8, 9, 10, 11  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
8theorem  ⊢  
 proveit.numbers.division.div_complex_closure
9instantiation12, 13, 14  ⊢  
  : , : , :
10instantiation61, 36, 15  ⊢  
  : , : , :
11instantiation16, 58  ⊢  
  :
12theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
13instantiation30, 22, 17  ⊢  
  : , :
14instantiation18, 19, 20  ⊢  
  : , : , :
15instantiation61, 39, 21  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17instantiation30, 28, 29  ⊢  
  : , :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation23, 63, 48, 24, 27, 25, 22, 28, 29  ⊢  
  : , : , : , : , : , :
20instantiation23, 24, 48, 25, 26, 27, 31, 32, 28, 29  ⊢  
  : , : , : , : , : , :
21instantiation61, 44, 55  ⊢  
  : , : , :
22instantiation30, 31, 32  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.multiplication.disassociation
24axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
25theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26instantiation33  ⊢  
  : , :
27instantiation33  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
29instantiation61, 36, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
31instantiation61, 36, 35  ⊢  
  : , : , :
32instantiation61, 36, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34instantiation61, 39, 38  ⊢  
  : , : , :
35instantiation61, 39, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
37instantiation61, 41, 42  ⊢  
  : , : , :
38instantiation61, 44, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation61, 44, 45  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
43instantiation61, 46, 47  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation61, 62, 48  ⊢  
  : , : , :
46instantiation49, 50, 51  ⊢  
  : , :
47instantiation52, 53, 58  ⊢  
  : , :
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
49theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
50theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
51instantiation54, 55, 56  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.modular.mod_natpos_in_interval
53assumption  ⊢  
54theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
55instantiation61, 57, 58  ⊢  
  : , : , :
56instantiation59, 60  ⊢  
  :
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
60instantiation61, 62, 63  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1