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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  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.negation.complex_closure
2instantiation3, 4, 5, 6  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_complex_closure
4instantiation7, 8, 9  ⊢  
  : , : , :
5instantiation45, 35, 10  ⊢  
  : , : , :
6instantiation11, 33  ⊢  
  :
7theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
8instantiation27, 18, 12  ⊢  
  : , :
9instantiation13, 14, 15  ⊢  
  : , : , :
10instantiation45, 38, 16  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
12instantiation27, 24, 25  ⊢  
  : , :
13axiom  ⊢  
 proveit.logic.equality.equals_transitivity
14instantiation19, 17, 47, 20, 23, 21, 18, 24, 25  ⊢  
  : , : , : , : , : , :
15instantiation19, 20, 47, 21, 22, 23, 28, 29, 24, 25  ⊢  
  : , : , : , : , : , :
16instantiation45, 43, 26  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
18instantiation27, 28, 29  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.multiplication.disassociation
20axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
21theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22instantiation30  ⊢  
  : , :
23instantiation30  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
25instantiation45, 35, 31  ⊢  
  : , : , :
26instantiation45, 32, 33  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
28instantiation45, 35, 34  ⊢  
  : , : , :
29instantiation45, 35, 36  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31instantiation45, 38, 37  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
33theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
34instantiation45, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation45, 40, 41  ⊢  
  : , : , :
37instantiation45, 43, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation45, 43, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation45, 46, 47  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2