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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  ⊢  
  : , : , : , : , :
6instantiation28, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation37, 16  ⊢  
  : , : , :
9instantiation37, 17  ⊢  
  : , : , :
10instantiation46, 24  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
12instantiation53, 19, 18  ⊢  
  : , : , :
13instantiation53, 19, 20  ⊢  
  : , : , :
14instantiation37, 21  ⊢  
  : , : , :
15instantiation37, 22  ⊢  
  : , : , :
16instantiation39, 23  ⊢  
  :
17instantiation39, 24  ⊢  
  :
18instantiation53, 26, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation53, 26, 27  ⊢  
  : , : , :
21instantiation28, 29, 30  ⊢  
  : , : , :
22instantiation37, 31  ⊢  
  : , : , :
23instantiation53, 51, 32  ⊢  
  : , : , :
24instantiation53, 51, 33  ⊢  
  : , : , :
25instantiation53, 35, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27instantiation53, 35, 36  ⊢  
  : , : , :
28axiom  ⊢  
 proveit.logic.equality.equals_transitivity
29instantiation37, 38  ⊢  
  : , : , :
30instantiation39, 47  ⊢  
  :
31instantiation40, 47  ⊢  
  :
32instantiation53, 42, 41  ⊢  
  : , : , :
33instantiation53, 42, 43  ⊢  
  : , : , :
34instantiation53, 44, 58  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36instantiation53, 44, 45  ⊢  
  : , : , :
37axiom  ⊢  
 proveit.logic.equality.substitution
38instantiation46, 47  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.division.frac_one_denom
40theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
41instantiation53, 49, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation53, 49, 50  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
46theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
47instantiation53, 51, 52  ⊢  
  : , : , :
48instantiation53, 54, 55  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
50theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52instantiation56, 57, 58  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
56theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
57instantiation59, 60  ⊢  
  : , :
58theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
59theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real