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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, ,  ⊢  
  : , : , :
1reference18  ⊢  
2instantiation34, 4,  ⊢  
  : , : , :
3instantiation8, 5, 6, ,  ⊢  
  : , : , :
4instantiation7, 42, 40,  ⊢  
  : , :
5instantiation8, 9, 10, ,  ⊢  
  : , : , :
6instantiation11, 12, 13, 14  ⊢  
  : , : , : , :
7theorem  ⊢  
 proveit.numbers.multiplication.commutation
8theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
9instantiation15, 40, 29, 16, 17, ,  ⊢  
  : , : , : , : , :
10instantiation18, 19, 20,  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
12instantiation34, 21  ⊢  
  : , : , :
13instantiation34, 22  ⊢  
  : , : , :
14instantiation41, 40  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_numer_left
16instantiation23, 42, 24,  ⊢  
  :
17instantiation52, 25, 26  ⊢  
  : , : , :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation34, 27,  ⊢  
  : , : , :
20instantiation34, 28  ⊢  
  : , : , :
21instantiation32, 40  ⊢  
  :
22instantiation32, 29  ⊢  
  :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
24assumption  ⊢  
25theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
26instantiation52, 30, 31  ⊢  
  : , : , :
27instantiation32, 33,  ⊢  
  :
28instantiation34, 35  ⊢  
  : , : , :
29instantiation52, 48, 36  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31instantiation52, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.division.frac_one_denom
33instantiation39, 40, 42,  ⊢  
  : , :
34axiom  ⊢  
 proveit.logic.equality.substitution
35instantiation41, 42  ⊢  
  :
36instantiation52, 43, 44  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38instantiation52, 45, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
40instantiation52, 48, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
42instantiation52, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
44instantiation52, 50, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49assumption  ⊢  
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.nat1