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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
2instantiation60, 14, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , :
4instantiation9, 53, 10, 11, 12  ⊢  
  : , :
5instantiation60, 20, 39  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
7instantiation60, 14, 13  ⊢  
  : , : , :
8instantiation60, 14, 15  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
10instantiation16  ⊢  
  : , :
11instantiation60, 18, 17  ⊢  
  : , : , :
12instantiation60, 18, 19  ⊢  
  : , : , :
13instantiation60, 20, 48  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
15instantiation60, 20, 31  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17instantiation60, 22, 21  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation60, 22, 23  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
21instantiation60, 25, 24  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
23instantiation60, 25, 26  ⊢  
  : , : , :
24instantiation60, 28, 27  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
26instantiation60, 28, 29  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
28theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
29instantiation30, 31, 32  ⊢  
  :
30theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
31instantiation60, 33, 41  ⊢  
  : , : , :
32instantiation34, 35, 36  ⊢  
  : , : , :
33instantiation37, 39, 40  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
35theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
36instantiation38, 39, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
38theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
39instantiation60, 52, 42  ⊢  
  : , : , :
40instantiation54, 43, 44  ⊢  
  : , :
41theorem  ⊢  
 proveit.physics.quantum.QPE._e_value_in_e_domain
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
43instantiation45, 48, 46  ⊢  
  : , :
44instantiation47, 48  ⊢  
  :
45theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
46instantiation49, 50, 51  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.negation.int_closure
48instantiation60, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
50instantiation54, 55, 56  ⊢  
  : , :
51instantiation57, 58  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
54theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
55instantiation60, 59, 64  ⊢  
  : , : , :
56instantiation60, 61, 62  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
58instantiation63, 64  ⊢  
  :
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
62instantiation65, 66  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
64axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
65theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
66theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1