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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  ⊢  
  : , : , : , : , :
6instantiation26, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation34, 16  ⊢  
  : , : , :
9instantiation34, 16  ⊢  
  : , : , :
10instantiation37, 22  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
12instantiation52, 18, 17  ⊢  
  : , : , :
13instantiation52, 18, 19  ⊢  
  : , : , :
14instantiation34, 20  ⊢  
  : , : , :
15instantiation34, 21  ⊢  
  : , : , :
16instantiation36, 22  ⊢  
  :
17instantiation52, 24, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation52, 24, 25  ⊢  
  : , : , :
20instantiation26, 27, 28  ⊢  
  : , : , :
21instantiation34, 29  ⊢  
  : , : , :
22instantiation52, 45, 30  ⊢  
  : , : , :
23instantiation52, 32, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
25instantiation52, 32, 33  ⊢  
  : , : , :
26axiom  ⊢  
 proveit.logic.equality.equals_transitivity
27instantiation34, 35  ⊢  
  : , : , :
28instantiation36, 43  ⊢  
  :
29instantiation37, 43  ⊢  
  :
30instantiation52, 48, 38  ⊢  
  : , : , :
31instantiation52, 40, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33instantiation52, 40, 41  ⊢  
  : , : , :
34axiom  ⊢  
 proveit.logic.equality.substitution
35instantiation42, 43  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.division.frac_one_denom
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
38instantiation52, 50, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
42theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
43instantiation52, 45, 46  ⊢  
  : , : , :
44instantiation52, 53, 47  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46instantiation52, 48, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
49instantiation52, 50, 51  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation52, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2