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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  ⊢  
  : , : , :
1reference65  ⊢  
2theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
3instantiation4, 5  ⊢  
  :
4theorem  ⊢  
 proveit.numbers.negation.real_closure
5instantiation6, 7, 8, 9  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.division.div_real_closure
7instantiation65, 19, 10  ⊢  
  : , : , :
8instantiation11, 12, 13  ⊢  
  : , :
9instantiation14, 58, 15, 16, 17  ⊢  
  : , :
10instantiation65, 25, 44  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
12instantiation65, 19, 18  ⊢  
  : , : , :
13instantiation65, 19, 20  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
15instantiation21  ⊢  
  : , :
16instantiation65, 23, 22  ⊢  
  : , : , :
17instantiation65, 23, 24  ⊢  
  : , : , :
18instantiation65, 25, 53  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
20instantiation65, 25, 36  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22instantiation65, 27, 26  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
24instantiation65, 27, 28  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
26instantiation65, 30, 29  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
28instantiation65, 30, 31  ⊢  
  : , : , :
29instantiation65, 33, 32  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
31instantiation65, 33, 34  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
33theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
34instantiation35, 36, 37  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
36instantiation65, 38, 46  ⊢  
  : , : , :
37instantiation39, 40, 41  ⊢  
  : , : , :
38instantiation42, 44, 45  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
40theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
41instantiation43, 44, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
43theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
44instantiation65, 57, 47  ⊢  
  : , : , :
45instantiation59, 48, 49  ⊢  
  : , :
46theorem  ⊢  
 proveit.physics.quantum.QPE._e_value_in_e_domain
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
48instantiation50, 53, 51  ⊢  
  : , :
49instantiation52, 53  ⊢  
  :
50theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
51instantiation54, 55, 56  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53instantiation65, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
55instantiation59, 60, 61  ⊢  
  : , :
56instantiation62, 63  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
59theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
60instantiation65, 64, 69  ⊢  
  : , : , :
61instantiation65, 66, 67  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
63instantiation68, 69  ⊢  
  :
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
65theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
67instantiation70, 71  ⊢  
  :
68theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
69axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
70theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
71theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1