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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  ⊢  
  : , : , :
1reference32  ⊢  
2instantiation6, 3, 4  ⊢  
  : , : , :
3instantiation32, 5  ⊢  
  : , : , :
4instantiation6, 7, 8  ⊢  
  : , : , :
5instantiation32, 9  ⊢  
  : , : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation10, 13, 88, 85, 15, 11, 16, 39, 55  ⊢  
  : , : , : , : , : , :
8instantiation12, 85, 88, 13, 14, 15, 16, 39, 55, 17*  ⊢  
  : , : , : , : , : , :
9instantiation18, 19, 20, 21  ⊢  
  : , : , : , :
10theorem  ⊢  
 proveit.numbers.addition.disassociation
11instantiation22  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.addition.association
13axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
14instantiation22  ⊢  
  : , :
15theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16instantiation23, 24, 25  ⊢  
  : , :
17instantiation26, 27, 28  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
19instantiation32, 29  ⊢  
  : , : , :
20instantiation30, 31  ⊢  
  : , :
21instantiation32, 33  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
24instantiation34, 55, 35, 36  ⊢  
  : , :
25instantiation48, 61, 41  ⊢  
  : , :
26theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
27instantiation37, 55, 61, 38  ⊢  
  : , : , :
28instantiation40, 55, 39  ⊢  
  : , :
29instantiation40, 41, 42  ⊢  
  : , :
30theorem  ⊢  
 proveit.logic.equality.equals_reversal
31instantiation43, 61, 44, 53, 50  ⊢  
  : , : , :
32axiom  ⊢  
 proveit.logic.equality.substitution
33instantiation45, 46, 47  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.division.div_complex_closure
35instantiation48, 61, 55  ⊢  
  : , :
36instantiation49, 50, 51  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
38theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
39instantiation86, 69, 52  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.addition.commutation
41instantiation86, 69, 53  ⊢  
  : , : , :
42instantiation54, 55  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
44instantiation56, 66  ⊢  
  :
45theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
46instantiation86, 57, 58  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
48theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
49theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
50instantiation59, 82  ⊢  
  :
51instantiation60, 61  ⊢  
  :
52instantiation86, 77, 62  ⊢  
  : , : , :
53instantiation63, 64, 65  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.negation.complex_closure
55instantiation86, 69, 66  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.negation.real_closure
57theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
58instantiation86, 67, 68  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
60theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
61instantiation86, 69, 70  ⊢  
  : , : , :
62instantiation86, 83, 71  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
64instantiation72, 73  ⊢  
  : , :
65axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
66instantiation86, 77, 74  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
68instantiation86, 75, 76  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
70instantiation86, 77, 78  ⊢  
  : , : , :
71instantiation79, 84  ⊢  
  :
72theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
74instantiation86, 83, 80  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
76instantiation86, 81, 82  ⊢  
  : , : , :
77theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
78instantiation86, 83, 84  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.numbers.negation.int_closure
80instantiation86, 87, 85  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
82theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
83theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
84instantiation86, 87, 88  ⊢  
  : , : , :
85theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
86theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
88theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements