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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,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_complex_closure
2instantiation16, 5, 6,  ⊢  
  : , : , :
3instantiation67, 39, 7  ⊢  
  : , : , :
4instantiation8, 9  ⊢  
  :
5instantiation32, 19, 10,  ⊢  
  : , :
6instantiation11, 12, 13,  ⊢  
  : , : , :
7instantiation67, 45, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
9instantiation15, 64, 61  ⊢  
  : , :
10instantiation16, 17, 18,  ⊢  
  : , : , :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation24, 69, 20, 25, 22, 26, 19, 33, 34, 28,  ⊢  
  : , : , : , : , : , :
13instantiation24, 25, 64, 20, 26, 21, 22, 29, 30, 33, 34, 28,  ⊢  
  : , : , : , : , : , :
14instantiation67, 48, 57  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
16theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
17instantiation32, 23, 28,  ⊢  
  : , :
18instantiation24, 25, 64, 69, 26, 27, 33, 34, 28,  ⊢  
  : , : , : , : , : , :
19instantiation32, 29, 30  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
21instantiation35  ⊢  
  : , :
22instantiation31  ⊢  
  : , : , :
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  ⊢  
  : , :
28instantiation67, 39, 36  ⊢  
  : , : , :
29instantiation67, 39, 37  ⊢  
  : , : , :
30instantiation67, 39, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34instantiation67, 39, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36instantiation67, 45, 41  ⊢  
  : , : , :
37instantiation67, 45, 42  ⊢  
  : , : , :
38instantiation67, 43, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation67, 45, 46  ⊢  
  : , : , :
41instantiation67, 48, 47  ⊢  
  : , : , :
42instantiation67, 48, 60  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation67, 48, 49  ⊢  
  : , : , :
47instantiation67, 51, 50  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
49instantiation67, 51, 52  ⊢  
  : , : , :
50assumption  ⊢  
51instantiation53, 54, 55  ⊢  
  : , :
52assumption  ⊢  
53theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
54theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
55instantiation56, 57, 58  ⊢  
  : , :
56theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
57instantiation59, 60, 61  ⊢  
  : , :
58instantiation62, 63  ⊢  
  :
59theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
60instantiation67, 68, 64  ⊢  
  : , : , :
61instantiation67, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.negation.int_closure
63instantiation67, 68, 69  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
65theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
66axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
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