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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, 24, 25, 12, 13, ,  ⊢  
  : , : , : , : , :
6instantiation29, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation37, 16  ⊢  
  : , : , :
9instantiation37, 17  ⊢  
  : , : , :
10instantiation44, 24  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
12instantiation50, 18, 19  ⊢  
  : , : , :
13instantiation20, 45, 21,  ⊢  
  :
14instantiation37, 22  ⊢  
  : , : , :
15instantiation37, 23  ⊢  
  : , : , :
16instantiation39, 24  ⊢  
  :
17instantiation39, 25  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation50, 26, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
21assumption  ⊢  
22instantiation37, 28  ⊢  
  : , : , :
23instantiation29, 30, 31  ⊢  
  : , : , :
24instantiation50, 48, 32  ⊢  
  : , : , :
25instantiation50, 48, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27instantiation50, 34, 35  ⊢  
  : , : , :
28instantiation36, 45  ⊢  
  :
29axiom  ⊢  
 proveit.logic.equality.equals_transitivity
30instantiation37, 38  ⊢  
  : , : , :
31instantiation39, 45  ⊢  
  :
32assumption  ⊢  
33instantiation50, 40, 41  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35instantiation50, 42, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
37axiom  ⊢  
 proveit.logic.equality.substitution
38instantiation44, 45  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.division.frac_one_denom
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation50, 46, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
44theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
45instantiation50, 48, 49  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
47instantiation50, 51, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49assumption  ⊢  
50theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1