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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10, 11, 12*  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.multiplication.commutation
7instantiation40, 27, 13  ⊢  
  : , : , :
8instantiation14, 15, 20, 16  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
10instantiation40, 17, 18  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
12instantiation19, 20  ⊢  
  :
13instantiation40, 21, 22  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.division.div_complex_closure
15instantiation40, 27, 23  ⊢  
  : , : , :
16instantiation24, 36  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18instantiation40, 25, 26  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
20instantiation40, 27, 28  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
22assumption  ⊢  
23instantiation40, 32, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
26instantiation40, 30, 31  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
28instantiation40, 32, 33  ⊢  
  : , : , :
29instantiation40, 37, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
31instantiation40, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
33instantiation40, 37, 38  ⊢  
  : , : , :
34instantiation40, 41, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
38instantiation40, 41, 42  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements