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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  ⊢  
  : , : , :
1reference9  ⊢  
2instantiation9, 3  ⊢  
  : , : , :
3instantiation4, 12, 25, 21, 5*  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_as_mult
5instantiation6, 7, 8  ⊢  
  : , : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation9, 10  ⊢  
  : , : , :
8instantiation11, 12, 13  ⊢  
  : , :
9axiom  ⊢  
 proveit.logic.equality.substitution
10instantiation14, 15, 16, 17*  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.multiplication.commutation
12instantiation45, 32, 18  ⊢  
  : , : , :
13instantiation19, 20, 25, 21  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
15instantiation45, 22, 23  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
17instantiation24, 25  ⊢  
  :
18instantiation45, 26, 27  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.division.div_complex_closure
20instantiation45, 32, 28  ⊢  
  : , : , :
21instantiation29, 41  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
23instantiation45, 30, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
25instantiation45, 32, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
27assumption  ⊢  
28instantiation45, 37, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31instantiation45, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation45, 37, 38  ⊢  
  : , : , :
34instantiation45, 42, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36instantiation45, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation45, 42, 43  ⊢  
  : , : , :
39instantiation45, 46, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43instantiation45, 46, 47  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
45theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements