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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.real_closure
2instantiation3, 4, 5, 6  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_real_closure
4instantiation72, 34, 7  ⊢  
  : , : , :
5instantiation8, 9, 10  ⊢  
  : , :
6instantiation11, 65, 12, 13, 14  ⊢  
  : , :
7instantiation72, 39, 51  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
9instantiation72, 34, 15  ⊢  
  : , : , :
10instantiation16, 17, 65  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
12instantiation18  ⊢  
  : , :
13instantiation72, 26, 19  ⊢  
  : , : , :
14instantiation20, 21, 22  ⊢  
  : , :
15instantiation72, 39, 23  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
17instantiation72, 34, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19instantiation72, 32, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
21instantiation72, 26, 27  ⊢  
  : , : , :
22instantiation72, 28, 29  ⊢  
  : , : , :
23instantiation72, 64, 30  ⊢  
  : , : , :
24instantiation72, 39, 43  ⊢  
  : , : , :
25instantiation72, 37, 31  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
27instantiation72, 32, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation72, 34, 35  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
31instantiation72, 40, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33instantiation72, 37, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation72, 39, 60  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38instantiation72, 40, 41  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
41instantiation42, 43, 44  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
43instantiation72, 45, 53  ⊢  
  : , : , :
44instantiation46, 47, 48  ⊢  
  : , : , :
45instantiation49, 51, 52  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
47theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
48instantiation50, 51, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
50theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
51instantiation72, 64, 54  ⊢  
  : , : , :
52instantiation66, 55, 56  ⊢  
  : , :
53theorem  ⊢  
 proveit.physics.quantum.QPE._e_value_in_e_domain
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55instantiation57, 60, 58  ⊢  
  : , :
56instantiation59, 60  ⊢  
  :
57theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
58instantiation61, 62, 63  ⊢  
  :
59theorem  ⊢  
 proveit.numbers.negation.int_closure
60instantiation72, 64, 65  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
62instantiation66, 67, 68  ⊢  
  : , :
63instantiation69, 70  ⊢  
  : , :
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
65theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
66theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
67instantiation72, 71, 76  ⊢  
  : , : , :
68instantiation72, 73, 74  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
70instantiation75, 76  ⊢  
  :
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
74instantiation77, 78  ⊢  
  :
75theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
76axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
77theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
78theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1