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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, 36, 25, 12, 13, ,  ⊢  
  : , : , : , : , :
6instantiation14, 15, 16,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation30, 17  ⊢  
  : , : , :
9instantiation30, 18  ⊢  
  : , : , :
10instantiation37, 36  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
12instantiation19, 38, 20,  ⊢  
  :
13instantiation48, 21, 22  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation30, 23,  ⊢  
  : , : , :
16instantiation30, 24  ⊢  
  : , : , :
17instantiation28, 36  ⊢  
  :
18instantiation28, 25  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
20assumption  ⊢  
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22instantiation48, 26, 27  ⊢  
  : , : , :
23instantiation28, 29,  ⊢  
  :
24instantiation30, 31  ⊢  
  : , : , :
25instantiation48, 44, 32  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27instantiation48, 33, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.division.frac_one_denom
29instantiation35, 36, 38,  ⊢  
  : , :
30axiom  ⊢  
 proveit.logic.equality.substitution
31instantiation37, 38  ⊢  
  :
32instantiation48, 39, 40  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34instantiation48, 41, 42  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
36instantiation48, 44, 43  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
38instantiation48, 44, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation48, 46, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
43assumption  ⊢  
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
45assumption  ⊢  
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
47instantiation48, 49, 50  ⊢  
  : , : , :
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