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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, 4, 5  ⊢  
  : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
2instantiation52, 7, 6  ⊢  
  : , : , :
3instantiation52, 7, 8  ⊢  
  : , : , :
4instantiation52, 10, 9  ⊢  
  : , : , :
5instantiation52, 10, 11  ⊢  
  : , : , :
6instantiation52, 13, 12  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
8instantiation52, 13, 14  ⊢  
  : , : , :
9instantiation52, 15, 16  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
11instantiation52, 17, 18  ⊢  
  : , : , :
12instantiation52, 19, 48  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
14instantiation52, 19, 20  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
16instantiation21, 22, 23  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
18instantiation52, 24, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
20instantiation52, 26, 27  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_pos_closure
22instantiation52, 28, 29  ⊢  
  : , : , :
23instantiation30, 31, 51  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
25instantiation52, 32, 33  ⊢  
  : , : , :
26instantiation34, 35, 36  ⊢  
  : , :
27assumption  ⊢  
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
29instantiation52, 37, 38  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
31instantiation39, 40  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
34theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
35theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
36instantiation41, 42, 43  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
38theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
39theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
41theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
42instantiation44, 45, 46  ⊢  
  : , :
43instantiation47, 48  ⊢  
  :
44theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
45instantiation52, 53, 49  ⊢  
  : , : , :
46instantiation52, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.negation.int_closure
48instantiation52, 53, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
50theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
51axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1