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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, , ,  ⊢  
  : , : , :
3instantiation12, 7, 8,  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
5instantiation9, 34, 23, 10, 11, , ,  ⊢  
  : , : , : , : , :
6instantiation12, 13, 14,  ⊢  
  : , : , :
7instantiation28, 15  ⊢  
  : , : , :
8instantiation28, 16  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
10instantiation17, 36, 18,  ⊢  
  :
11instantiation40, 19, 20  ⊢  
  : , : , :
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation28, 21,  ⊢  
  : , : , :
14instantiation28, 22  ⊢  
  : , : , :
15instantiation26, 34  ⊢  
  :
16instantiation26, 23  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
18assumption  ⊢  
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation40, 24, 25  ⊢  
  : , : , :
21instantiation26, 27,  ⊢  
  :
22instantiation28, 29  ⊢  
  : , : , :
23instantiation40, 41, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
25instantiation40, 31, 32  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.division.frac_one_denom
27instantiation33, 34, 36,  ⊢  
  : , :
28axiom  ⊢  
 proveit.logic.equality.substitution
29instantiation35, 36  ⊢  
  :
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
32instantiation40, 37, 38  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
34instantiation40, 41, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
36instantiation40, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
38theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
39assumption  ⊢  
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
42assumption  ⊢