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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, 6*, 7*,  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
2reference15  ⊢  
3instantiation8, 9, 10  ⊢  
  : , : , :
4instantiation72, 12, 11  ⊢  
  : , : , :
5instantiation72, 12, 13  ⊢  
  : , : , :
6instantiation14, 15  ⊢  
  :
7instantiation16, 17  ⊢  
  :
8theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
9instantiation40, 27, 18  ⊢  
  : , :
10instantiation19, 20, 21  ⊢  
  : , : , :
11instantiation72, 23, 22  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
13instantiation72, 23, 24  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.division.frac_one_denom
15instantiation72, 49, 25  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
17instantiation72, 49, 26  ⊢  
  : , : , :
18instantiation40, 33, 34  ⊢  
  : , :
19axiom  ⊢  
 proveit.logic.equality.equals_transitivity
20instantiation28, 74, 67, 29, 32, 30, 27, 33, 34  ⊢  
  : , : , : , : , : , :
21instantiation28, 29, 67, 30, 31, 32, 41, 42, 33, 34  ⊢  
  : , : , : , : , : , :
22instantiation72, 36, 35  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
24instantiation72, 36, 37  ⊢  
  : , : , :
25instantiation72, 54, 38  ⊢  
  : , : , :
26instantiation72, 54, 39  ⊢  
  : , : , :
27instantiation40, 41, 42  ⊢  
  : , :
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
31instantiation43  ⊢  
  : , :
32instantiation43  ⊢  
  : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34instantiation72, 49, 44  ⊢  
  : , : , :
35instantiation72, 46, 45  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37instantiation72, 46, 69  ⊢  
  : , : , :
38instantiation72, 62, 47  ⊢  
  : , : , :
39instantiation72, 62, 65  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
41instantiation72, 49, 48  ⊢  
  : , : , :
42instantiation72, 49, 50  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44instantiation72, 54, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
47instantiation72, 52, 53  ⊢  
  : , : , :
48instantiation72, 54, 55  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation72, 56, 57  ⊢  
  : , : , :
51instantiation72, 62, 58  ⊢  
  : , : , :
52instantiation59, 60, 61  ⊢  
  : , :
53assumption  ⊢  
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
55instantiation72, 62, 63  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
58assumption  ⊢  
59theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
60theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
61instantiation64, 65, 66  ⊢  
  : , :
62theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
63instantiation72, 73, 67  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
65instantiation72, 68, 69  ⊢  
  : , : , :
66instantiation70, 71  ⊢  
  :
67theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
69theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
70theorem  ⊢  
 proveit.numbers.negation.int_closure
71instantiation72, 73, 74  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements