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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,  ⊢  
  : , : , :
1reference5  ⊢  
2instantiation33, 3, 4,  ⊢  
  : , : , :
3instantiation5, 6,  ⊢  
  : , : , :
4instantiation7, 8,  ⊢  
  : , :
5axiom  ⊢  
 proveit.logic.equality.substitution
6instantiation33, 9, 10,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.equals_reversal
8instantiation11, 12, 13, 14,  ⊢  
  : , :
9instantiation15, 16, 39, 42, 17, 43, 50, 51, 46, 21, 47,  ⊢  
  : , : , : , : , : , : , :
10instantiation18, 42, 19, 39, 43, 20, 50, 51, 46, 47, 21,  ⊢  
  : , : , : , : , : , :
11instantiation22, 48  ⊢  
  :
12instantiation65, 55, 23  ⊢  
  : , : , :
13instantiation24, 25, 26  ⊢  
  : , : , :
14instantiation27, 28  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.multiplication.rightward_commutation
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
17instantiation29  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.multiplication.association
19theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
20instantiation30  ⊢  
  : , : , : , :
21instantiation65, 55, 31  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.int_exp_of_exp
23instantiation65, 60, 37  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
25instantiation49, 40, 32  ⊢  
  : , :
26instantiation33, 34, 35  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
28instantiation65, 36, 37  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
31instantiation65, 58, 38  ⊢  
  : , : , :
32instantiation49, 46, 47  ⊢  
  : , :
33axiom  ⊢  
 proveit.logic.equality.equals_transitivity
34instantiation41, 39, 67, 42, 45, 43, 40, 46, 47  ⊢  
  : , : , : , : , : , :
35instantiation41, 42, 67, 43, 44, 45, 50, 51, 46, 47  ⊢  
  : , : , : , : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
38instantiation65, 63, 48  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40instantiation49, 50, 51  ⊢  
  : , :
41theorem  ⊢  
 proveit.numbers.multiplication.disassociation
42axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
43theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
44instantiation52  ⊢  
  : , :
45instantiation52  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
47instantiation65, 55, 53  ⊢  
  : , : , :
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
50instantiation65, 55, 54  ⊢  
  : , : , :
51instantiation65, 55, 56  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
53instantiation65, 58, 57  ⊢  
  : , : , :
54instantiation65, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
56instantiation65, 60, 61  ⊢  
  : , : , :
57instantiation65, 63, 62  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
59instantiation65, 63, 64  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
62assumption  ⊢  
63theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
64instantiation65, 66, 67  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
67theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2