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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, , ,  ⊢  
  : , :
1theorem  ⊢  
 proveit.logic.equality.equals_reversal
2instantiation5, 3, 4, , ,  ⊢  
  : , : , :
3instantiation5, 6, 7, , ,  ⊢  
  : , : , :
4instantiation11, 8, 77, 9, 15, 17, 18, 19, 10, 21, 22, , ,  ⊢  
  : , : , : , : , : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation11, 80, 12, 13, 18, 19, 50, 21, 20, 22, , ,  ⊢  
  : , : , : , : , : , : , :
7instantiation14, 77, 15, 16, 17, 18, 19, 50, 20, 21, 22, 23*, , ,  ⊢  
  : , : , : , : , : , :
8axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation30, 24, 52, 31  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
13instantiation25  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.multiplication.association
15instantiation26  ⊢  
  : , :
16instantiation26  ⊢  
  : , :
17instantiation26  ⊢  
  : , :
18instantiation78, 61, 27  ⊢  
  : , : , :
19instantiation28, 29  ⊢  
  :
20instantiation30, 50, 52, 31  ⊢  
  : , :
21instantiation32, 33, 50  ⊢  
  : , :
22instantiation78, 61, 34  ⊢  
  : , : , :
23instantiation35, 50, 36, 37, 38*, 39*, 40*  ⊢  
  : , : , : , :
24instantiation78, 61, 41  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
26theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27instantiation78, 55, 42  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
29instantiation78, 61, 43  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.division.div_complex_closure
31instantiation44, 73  ⊢  
  :
32theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
33instantiation78, 61, 45  ⊢  
  : , : , :
34assumption  ⊢  
35theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
36instantiation78, 47, 46  ⊢  
  : , : , :
37instantiation78, 47, 48  ⊢  
  : , : , :
38instantiation49, 50  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
40instantiation51, 52  ⊢  
  :
41instantiation78, 68, 53  ⊢  
  : , : , :
42assumption  ⊢  
43instantiation78, 55, 54  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
45instantiation78, 55, 56  ⊢  
  : , : , :
46instantiation78, 58, 57  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
48instantiation78, 58, 59  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.division.frac_one_denom
50instantiation78, 61, 60  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
52instantiation78, 61, 62  ⊢  
  : , : , :
53instantiation78, 75, 63  ⊢  
  : , : , :
54assumption  ⊢  
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
56assumption  ⊢  
57instantiation78, 65, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
59instantiation78, 65, 66  ⊢  
  : , : , :
60instantiation78, 68, 67  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
62instantiation78, 68, 69  ⊢  
  : , : , :
63instantiation78, 79, 70  ⊢  
  : , : , :
64instantiation78, 72, 71  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
66instantiation78, 72, 73  ⊢  
  : , : , :
67instantiation78, 75, 74  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
69instantiation78, 75, 76  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
71theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
72theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
73theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
74instantiation78, 79, 77  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
76instantiation78, 79, 80  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
78theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
80theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
*equality replacement requirements