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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation4, 5, 6, 7  ⊢  
  : , : , : , : , :
3instantiation21, 8, 9  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
5instantiation44, 38, 10  ⊢  
  : , : , :
6instantiation44, 12, 11  ⊢  
  : , : , :
7instantiation44, 12, 13  ⊢  
  : , : , :
8instantiation29, 14  ⊢  
  : , : , :
9instantiation29, 15  ⊢  
  : , : , :
10instantiation44, 40, 16  ⊢  
  : , : , :
11instantiation44, 18, 17  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
13instantiation44, 18, 19  ⊢  
  : , : , :
14instantiation29, 20  ⊢  
  : , : , :
15instantiation21, 22, 23  ⊢  
  : , : , :
16instantiation44, 42, 24  ⊢  
  : , : , :
17instantiation44, 26, 25  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
19instantiation44, 26, 27  ⊢  
  : , : , :
20instantiation28, 37  ⊢  
  :
21axiom  ⊢  
 proveit.logic.equality.equals_transitivity
22instantiation29, 30  ⊢  
  : , : , :
23instantiation31, 37  ⊢  
  :
24instantiation44, 45, 32  ⊢  
  : , : , :
25instantiation44, 34, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
27instantiation44, 34, 35  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
29axiom  ⊢  
 proveit.logic.equality.substitution
30instantiation36, 37  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.division.frac_one_denom
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
34theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
35theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
36theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
37instantiation44, 38, 39  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation44, 40, 41  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation44, 42, 43  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43instantiation44, 45, 46  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3