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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, 24, 25, 12, 13  ⊢  
  : , : , : , : , :
6instantiation31, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation41, 16  ⊢  
  : , : , :
9instantiation41, 17  ⊢  
  : , : , :
10instantiation50, 25  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
12instantiation18, 51, 19  ⊢  
  :
13instantiation77, 20, 21  ⊢  
  : , : , :
14instantiation41, 22  ⊢  
  : , : , :
15instantiation41, 23  ⊢  
  : , : , :
16instantiation43, 24  ⊢  
  :
17instantiation43, 25  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
19instantiation26, 27, 28  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21instantiation77, 29, 30  ⊢  
  : , : , :
22instantiation31, 32, 33  ⊢  
  : , : , :
23instantiation41, 34  ⊢  
  : , : , :
24instantiation77, 53, 35  ⊢  
  : , : , :
25instantiation77, 53, 36  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
27instantiation77, 39, 37  ⊢  
  : , : , :
28instantiation77, 39, 38  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30instantiation77, 39, 40  ⊢  
  : , : , :
31axiom  ⊢  
 proveit.logic.equality.equals_transitivity
32instantiation41, 42  ⊢  
  : , : , :
33instantiation43, 51  ⊢  
  :
34instantiation44, 51  ⊢  
  :
35instantiation77, 58, 45  ⊢  
  : , : , :
36instantiation77, 58, 46  ⊢  
  : , : , :
37instantiation77, 48, 47  ⊢  
  : , : , :
38instantiation77, 48, 76  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
40instantiation77, 48, 49  ⊢  
  : , : , :
41axiom  ⊢  
 proveit.logic.equality.substitution
42instantiation50, 51  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.division.frac_one_denom
44theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
45instantiation77, 62, 73  ⊢  
  : , : , :
46instantiation77, 62, 52  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
50theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
51instantiation77, 53, 54  ⊢  
  : , : , :
52instantiation55, 56, 57  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
54instantiation77, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
56instantiation60, 61  ⊢  
  : , :
57theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_in_m_domain
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
59instantiation77, 62, 67  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
61instantiation63, 64, 65  ⊢  
  : , :
62theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
63theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
64theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
65instantiation66, 67, 68  ⊢  
  : , :
66theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
67instantiation69, 70, 71  ⊢  
  : , :
68instantiation72, 73  ⊢  
  :
69theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
70instantiation77, 78, 74  ⊢  
  : , : , :
71instantiation77, 75, 76  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.negation.int_closure
73instantiation77, 78, 79  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
75theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
76axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
77theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
79theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1