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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  ⊢  
  : , : , :
1reference73  ⊢  
2reference29  ⊢  
3instantiation4, 5, 6, 7  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_real_closure
5instantiation73, 35, 8  ⊢  
  : , : , :
6instantiation9, 10, 11  ⊢  
  : , :
7instantiation12, 66, 13, 14, 15  ⊢  
  : , :
8instantiation73, 40, 52  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
10instantiation73, 35, 16  ⊢  
  : , : , :
11instantiation17, 18, 66  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
13instantiation19  ⊢  
  : , :
14instantiation73, 27, 20  ⊢  
  : , : , :
15instantiation21, 22, 23  ⊢  
  : , :
16instantiation73, 40, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
18instantiation73, 35, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20instantiation73, 33, 26  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
22instantiation73, 27, 28  ⊢  
  : , : , :
23instantiation73, 29, 30  ⊢  
  : , : , :
24instantiation73, 65, 31  ⊢  
  : , : , :
25instantiation73, 40, 44  ⊢  
  : , : , :
26instantiation73, 38, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
28instantiation73, 33, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
30instantiation73, 35, 36  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
32instantiation73, 41, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
34instantiation73, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation73, 40, 61  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39instantiation73, 41, 42  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
42instantiation43, 44, 45  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
44instantiation73, 46, 54  ⊢  
  : , : , :
45instantiation47, 48, 49  ⊢  
  : , : , :
46instantiation50, 52, 53  ⊢  
  : , :
47theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
48theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
49instantiation51, 52, 53, 54  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
51theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
52instantiation73, 65, 55  ⊢  
  : , : , :
53instantiation67, 56, 57  ⊢  
  : , :
54theorem  ⊢  
 proveit.physics.quantum.QPE._e_value_in_e_domain
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
56instantiation58, 61, 59  ⊢  
  : , :
57instantiation60, 61  ⊢  
  :
58theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
59instantiation62, 63, 64  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.negation.int_closure
61instantiation73, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
63instantiation67, 68, 69  ⊢  
  : , :
64instantiation70, 71  ⊢  
  : , :
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
67theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
68instantiation73, 72, 77  ⊢  
  : , : , :
69instantiation73, 74, 75  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
71instantiation76, 77  ⊢  
  :
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
73theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
75instantiation78, 79  ⊢  
  :
76theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
77axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
78theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
79theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1