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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, 22, 12, 13  ⊢  
  : , : , : , : , :
6instantiation27, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation35, 16  ⊢  
  : , : , :
9instantiation35, 16  ⊢  
  : , : , :
10instantiation42, 22  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
12instantiation48, 18, 17  ⊢  
  : , : , :
13instantiation48, 18, 19  ⊢  
  : , : , :
14instantiation35, 20  ⊢  
  : , : , :
15instantiation35, 21  ⊢  
  : , : , :
16instantiation37, 22  ⊢  
  :
17instantiation48, 24, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation48, 24, 25  ⊢  
  : , : , :
20instantiation35, 26  ⊢  
  : , : , :
21instantiation27, 28, 29  ⊢  
  : , : , :
22instantiation48, 46, 30  ⊢  
  : , : , :
23instantiation48, 32, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
25instantiation48, 32, 33  ⊢  
  : , : , :
26instantiation34, 43  ⊢  
  :
27axiom  ⊢  
 proveit.logic.equality.equals_transitivity
28instantiation35, 36  ⊢  
  : , : , :
29instantiation37, 43  ⊢  
  :
30instantiation48, 38, 39  ⊢  
  : , : , :
31instantiation48, 41, 40  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33instantiation48, 41, 53  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
35axiom  ⊢  
 proveit.logic.equality.substitution
36instantiation42, 43  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.division.frac_one_denom
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation48, 44, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
42theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
43instantiation48, 46, 47  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation48, 49, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation51, 52, 53  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
51theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
52instantiation54, 55  ⊢  
  : , :
53theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
54theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real