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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_real_closure
2instantiation70, 32, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , :
4instantiation9, 63, 10, 11, 12  ⊢  
  : , :
5instantiation70, 37, 49  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
7instantiation70, 32, 13  ⊢  
  : , : , :
8instantiation14, 15, 63  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
10instantiation16  ⊢  
  : , :
11instantiation70, 24, 17  ⊢  
  : , : , :
12instantiation18, 19, 20  ⊢  
  : , :
13instantiation70, 37, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
15instantiation70, 32, 22  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17instantiation70, 30, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
19instantiation70, 24, 25  ⊢  
  : , : , :
20instantiation70, 26, 27  ⊢  
  : , : , :
21instantiation70, 62, 28  ⊢  
  : , : , :
22instantiation70, 37, 41  ⊢  
  : , : , :
23instantiation70, 35, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
25instantiation70, 30, 31  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
27instantiation70, 32, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
29instantiation70, 38, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31instantiation70, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
33instantiation70, 37, 58  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36instantiation70, 38, 39  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39instantiation40, 41, 42  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
41instantiation70, 43, 51  ⊢  
  : , : , :
42instantiation44, 45, 46  ⊢  
  : , : , :
43instantiation47, 49, 50  ⊢  
  : , :
44theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
45theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
46instantiation48, 49, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
48theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
49instantiation70, 62, 52  ⊢  
  : , : , :
50instantiation64, 53, 54  ⊢  
  : , :
51theorem  ⊢  
 proveit.physics.quantum.QPE._e_value_in_e_domain
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
53instantiation55, 58, 56  ⊢  
  : , :
54instantiation57, 58  ⊢  
  :
55theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
56instantiation59, 60, 61  ⊢  
  :
57theorem  ⊢  
 proveit.numbers.negation.int_closure
58instantiation70, 62, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
60instantiation64, 65, 66  ⊢  
  : , :
61instantiation67, 68  ⊢  
  : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
64theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
65instantiation70, 69, 74  ⊢  
  : , : , :
66instantiation70, 71, 72  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
68instantiation73, 74  ⊢  
  :
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
70theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
72instantiation75, 76  ⊢  
  :
73theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
74axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
75theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
76theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1