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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  ⊢  
  : , : , :
3instantiation7, 12, 68, 76, 14, 8, 25, 15, 39, 21, 9  ⊢  
  : , : , : , : , : , : , : , :
4axiom  ⊢  
 proveit.logic.equality.equals_transitivity
5instantiation11, 12, 76, 68, 14, 13, 25, 15, 10  ⊢  
  : , : , : , : , : , :
6instantiation11, 76, 18, 12, 13, 19, 14, 25, 15, 20, 39, 21  ⊢  
  : , : , : , : , : , :
7theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general
8instantiation22  ⊢  
  : , :
9instantiation16  ⊢  
  :
10instantiation17, 18, 19, 20, 39, 21  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.addition.disassociation
12axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
13instantiation22  ⊢  
  : , :
14theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15instantiation74, 56, 23  ⊢  
  : , : , :
16axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
17theorem  ⊢  
 proveit.numbers.addition.add_complex_closure
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
19instantiation24  ⊢  
  : , : , :
20instantiation26, 25  ⊢  
  :
21instantiation26, 27  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23instantiation74, 63, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
25instantiation29, 30, 31  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.negation.complex_closure
27instantiation74, 56, 32  ⊢  
  : , : , :
28instantiation74, 69, 67  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
30instantiation33, 39, 34, 35  ⊢  
  : , :
31instantiation38, 49, 36  ⊢  
  : , :
32instantiation74, 63, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.division.div_complex_closure
34instantiation38, 49, 39  ⊢  
  : , :
35instantiation40, 41, 42  ⊢  
  : , : , :
36instantiation74, 56, 43  ⊢  
  : , : , :
37instantiation74, 69, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
39instantiation74, 56, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
41instantiation46, 47  ⊢  
  :
42instantiation48, 49  ⊢  
  :
43instantiation50, 51, 52  ⊢  
  : , : , :
44instantiation74, 53, 54  ⊢  
  : , : , :
45instantiation74, 63, 55  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
47theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
48theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
49instantiation74, 56, 57  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
51instantiation58, 59  ⊢  
  : , :
52axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
53instantiation60, 62, 61  ⊢  
  : , :
54assumption  ⊢  
55instantiation74, 69, 62  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
57instantiation74, 63, 64  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
61instantiation65, 66, 67  ⊢  
  : , :
62instantiation74, 75, 68  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
64instantiation74, 69, 73  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
66instantiation74, 70, 71  ⊢  
  : , : , :
67instantiation72, 73  ⊢  
  :
68theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
69theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
71theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
72theorem  ⊢  
 proveit.numbers.negation.int_closure
73instantiation74, 75, 76  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2