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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  ⊢  
  : , : , :
1reference4  ⊢  
2instantiation4, 5, 6  ⊢  
  : , : , :
3instantiation7, 8, 9, 10  ⊢  
  : , : , : , :
4theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
5instantiation11, 23, 24, 12, 13  ⊢  
  : , : , : , : , :
6instantiation29, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation40, 16  ⊢  
  : , : , :
9instantiation40, 17  ⊢  
  : , : , :
10instantiation52, 24  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
12instantiation80, 19, 18  ⊢  
  : , : , :
13instantiation80, 19, 20  ⊢  
  : , : , :
14instantiation40, 21  ⊢  
  : , : , :
15instantiation40, 22  ⊢  
  : , : , :
16instantiation42, 23  ⊢  
  :
17instantiation42, 24  ⊢  
  :
18instantiation80, 25, 26  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation80, 27, 28  ⊢  
  : , : , :
21instantiation29, 30, 31  ⊢  
  : , : , :
22instantiation40, 32  ⊢  
  : , : , :
23instantiation80, 59, 33  ⊢  
  : , : , :
24instantiation80, 59, 34  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
26instantiation35, 36, 37  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
28instantiation80, 38, 39  ⊢  
  : , : , :
29axiom  ⊢  
 proveit.logic.equality.equals_transitivity
30instantiation40, 41  ⊢  
  : , : , :
31instantiation42, 53  ⊢  
  :
32instantiation43, 53  ⊢  
  :
33instantiation80, 63, 44  ⊢  
  : , : , :
34instantiation80, 63, 45  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_pos_closure
36instantiation80, 46, 47  ⊢  
  : , : , :
37instantiation48, 49, 79  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39instantiation80, 50, 51  ⊢  
  : , : , :
40axiom  ⊢  
 proveit.logic.equality.substitution
41instantiation52, 53  ⊢  
  :
42theorem  ⊢  
 proveit.numbers.division.frac_one_denom
43theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
44instantiation80, 68, 76  ⊢  
  : , : , :
45instantiation80, 68, 54  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
47instantiation80, 55, 56  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
49instantiation57, 58  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
52theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
53instantiation80, 59, 60  ⊢  
  : , : , :
54instantiation80, 61, 62  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
56theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
57theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
59theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
60instantiation80, 63, 64  ⊢  
  : , : , :
61instantiation65, 66, 67  ⊢  
  : , :
62assumption  ⊢  
63theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
64instantiation80, 68, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
66theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
67instantiation69, 70, 71  ⊢  
  : , :
68theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
69theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
70instantiation72, 73, 74  ⊢  
  : , :
71instantiation75, 76  ⊢  
  :
72theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
73instantiation80, 81, 77  ⊢  
  : , : , :
74instantiation80, 78, 79  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.negation.int_closure
76instantiation80, 81, 82  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
78theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
79axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
80theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
81theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
82theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1