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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, , ,  ⊢  
  : , : , :
1reference4  ⊢  
2instantiation4, 5, 6, , ,  ⊢  
  : , : , :
3instantiation10, 7, 76, 8, 14, 16, 17, 18, 9, 20, 21, , ,  ⊢  
  : , : , : , : , : , : , :
4axiom  ⊢  
 proveit.logic.equality.equals_transitivity
5instantiation10, 79, 11, 12, 17, 18, 49, 20, 19, 21, , ,  ⊢  
  : , : , : , : , : , : , :
6instantiation13, 76, 14, 15, 16, 17, 18, 49, 19, 20, 21, 22*, , ,  ⊢  
  : , : , : , : , : , :
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9instantiation29, 23, 51, 30  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
11theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
12instantiation24  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.multiplication.association
14instantiation25  ⊢  
  : , :
15instantiation25  ⊢  
  : , :
16instantiation25  ⊢  
  : , :
17instantiation77, 60, 26  ⊢  
  : , : , :
18instantiation27, 28  ⊢  
  :
19instantiation29, 49, 51, 30  ⊢  
  : , :
20instantiation31, 32, 49  ⊢  
  : , :
21instantiation77, 60, 33  ⊢  
  : , : , :
22instantiation34, 49, 35, 36, 37*, 38*, 39*  ⊢  
  : , : , : , :
23instantiation77, 60, 40  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
25theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26instantiation77, 54, 41  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
28instantiation77, 60, 42  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.division.div_complex_closure
30instantiation43, 72  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
32instantiation77, 60, 44  ⊢  
  : , : , :
33assumption  ⊢  
34theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
35instantiation77, 46, 45  ⊢  
  : , : , :
36instantiation77, 46, 47  ⊢  
  : , : , :
37instantiation48, 49  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
39instantiation50, 51  ⊢  
  :
40instantiation77, 67, 52  ⊢  
  : , : , :
41assumption  ⊢  
42instantiation77, 54, 53  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
44instantiation77, 54, 55  ⊢  
  : , : , :
45instantiation77, 57, 56  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
47instantiation77, 57, 58  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.division.frac_one_denom
49instantiation77, 60, 59  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
51instantiation77, 60, 61  ⊢  
  : , : , :
52instantiation77, 74, 62  ⊢  
  : , : , :
53assumption  ⊢  
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
55assumption  ⊢  
56instantiation77, 64, 63  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
58instantiation77, 64, 65  ⊢  
  : , : , :
59instantiation77, 67, 66  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
61instantiation77, 67, 68  ⊢  
  : , : , :
62instantiation77, 78, 69  ⊢  
  : , : , :
63instantiation77, 71, 70  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
65instantiation77, 71, 72  ⊢  
  : , : , :
66instantiation77, 74, 73  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
68instantiation77, 74, 75  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
70theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
72theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
73instantiation77, 78, 76  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
75instantiation77, 78, 79  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
77theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
79theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
*equality replacement requirements