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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
2instantiation3, 4, 5, 6,  ⊢  
  : , :
3instantiation7, 8  ⊢  
  :
4instantiation65, 55, 9  ⊢  
  : , : , :
5instantiation10, 11, 12, 13  ⊢  
  : , :
6instantiation14, 15  ⊢  
  :
7theorem  ⊢  
 proveit.numbers.exponentiation.int_exp_of_neg_exp
8instantiation65, 16, 17  ⊢  
  : , : , :
9instantiation65, 60, 24  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.division.div_complex_closure
11instantiation18, 19, 20  ⊢  
  : , : , :
12instantiation65, 55, 21  ⊢  
  : , : , :
13instantiation22, 52  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
15instantiation65, 23, 24  ⊢  
  : , : , :
16instantiation25, 26, 27  ⊢  
  : , :
17assumption  ⊢  
18theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
19instantiation46, 35, 28  ⊢  
  : , :
20instantiation29, 30, 31  ⊢  
  : , : , :
21instantiation65, 58, 32  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
25theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
26theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
27instantiation33, 43, 34  ⊢  
  : , :
28instantiation46, 41, 42  ⊢  
  : , :
29axiom  ⊢  
 proveit.logic.equality.equals_transitivity
30instantiation36, 53, 67, 37, 40, 38, 35, 41, 42  ⊢  
  : , : , : , : , : , :
31instantiation36, 37, 67, 38, 39, 40, 47, 48, 41, 42  ⊢  
  : , : , : , : , : , :
32instantiation65, 63, 43  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
34instantiation44, 45  ⊢  
  :
35instantiation46, 47, 48  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.multiplication.disassociation
37axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
38theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39instantiation49  ⊢  
  : , :
40instantiation49  ⊢  
  : , :
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
42instantiation65, 55, 50  ⊢  
  : , : , :
43instantiation65, 51, 52  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.negation.int_closure
45instantiation65, 66, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
47instantiation65, 55, 54  ⊢  
  : , : , :
48instantiation65, 55, 56  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50instantiation65, 58, 57  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
52theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
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