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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
2instantiation50, 40, 4  ⊢  
  : , : , :
3instantiation5, 6  ⊢  
  :
4instantiation50, 45, 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  ⊢  
  : , : , :
10instantiation50, 40, 15  ⊢  
  : , : , :
11instantiation16, 38  ⊢  
  :
12theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
13instantiation32, 23, 17  ⊢  
  : , :
14instantiation18, 19, 20  ⊢  
  : , : , :
15instantiation50, 43, 21  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17instantiation32, 29, 30  ⊢  
  : , :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation24, 22, 52, 25, 28, 26, 23, 29, 30  ⊢  
  : , : , : , : , : , :
20instantiation24, 25, 52, 26, 27, 28, 33, 34, 29, 30  ⊢  
  : , : , : , : , : , :
21instantiation50, 48, 31  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
23instantiation32, 33, 34  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.multiplication.disassociation
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27instantiation35  ⊢  
  : , :
28instantiation35  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
30instantiation50, 40, 36  ⊢  
  : , : , :
31instantiation50, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
33instantiation50, 40, 39  ⊢  
  : , : , :
34instantiation50, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36instantiation50, 43, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
38theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
39instantiation50, 43, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41instantiation50, 45, 46  ⊢  
  : , : , :
42instantiation50, 48, 47  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
44instantiation50, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
49instantiation50, 51, 52  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2