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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, 4, 5, 6, 7, 8, 9, 10, 11, 12*, , ,  ⊢  
  : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.multiplication.association
2reference60  ⊢  
3instantiation13  ⊢  
  : , :
4instantiation13  ⊢  
  : , :
5instantiation13  ⊢  
  : , :
6instantiation61, 46, 14  ⊢  
  : , : , :
7instantiation15, 16  ⊢  
  :
8reference36  ⊢  
9instantiation17, 36, 38, 18  ⊢  
  : , :
10instantiation19, 20, 36  ⊢  
  : , :
11instantiation61, 46, 21  ⊢  
  : , : , :
12instantiation22, 36, 23, 24, 25*, 26*, 27*  ⊢  
  : , : , : , :
13theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14instantiation61, 40, 28  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
16instantiation61, 46, 29  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.division.div_complex_closure
18instantiation30, 56  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
20instantiation61, 46, 31  ⊢  
  : , : , :
21assumption  ⊢  
22theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
23instantiation61, 33, 32  ⊢  
  : , : , :
24instantiation61, 33, 34  ⊢  
  : , : , :
25instantiation35, 36  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
27instantiation37, 38  ⊢  
  :
28assumption  ⊢  
29instantiation61, 40, 39  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31instantiation61, 40, 41  ⊢  
  : , : , :
32instantiation61, 43, 42  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
34instantiation61, 43, 44  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.division.frac_one_denom
36instantiation61, 46, 45  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
38instantiation61, 46, 47  ⊢  
  : , : , :
39assumption  ⊢  
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
41assumption  ⊢  
42instantiation61, 49, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
44instantiation61, 49, 50  ⊢  
  : , : , :
45instantiation61, 52, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
47instantiation61, 52, 53  ⊢  
  : , : , :
48instantiation61, 55, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50instantiation61, 55, 56  ⊢  
  : , : , :
51instantiation61, 58, 57  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation61, 58, 59  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
57instantiation61, 62, 60  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
59instantiation61, 62, 63  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
*equality replacement requirements