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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, 94, 91, 15, 11, 16, 40, 49  ⊢  
  : , : , : , : , : , :
8instantiation12, 91, 94, 13, 14, 15, 16, 40, 49, 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, 49, 35, 36  ⊢  
  : , :
25instantiation92, 71, 37  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
27instantiation38, 49, 62, 39  ⊢  
  : , : , :
28instantiation41, 49, 40  ⊢  
  : , :
29instantiation41, 42, 43  ⊢  
  : , :
30theorem  ⊢  
 proveit.logic.equality.equals_reversal
31instantiation44, 62, 56, 55, 51  ⊢  
  : , : , :
32axiom  ⊢  
 proveit.logic.equality.substitution
33instantiation45, 46, 47  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.division.div_complex_closure
35instantiation48, 62, 49  ⊢  
  : , :
36instantiation50, 51, 52  ⊢  
  : , : , :
37instantiation92, 81, 53  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
39theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
40instantiation92, 71, 54  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.addition.commutation
42instantiation92, 71, 55  ⊢  
  : , : , :
43instantiation92, 71, 56  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
45theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
46instantiation92, 57, 58  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
48theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
49instantiation92, 71, 59  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
51instantiation60, 88  ⊢  
  :
52instantiation61, 62  ⊢  
  :
53instantiation92, 89, 63  ⊢  
  : , : , :
54instantiation92, 81, 64  ⊢  
  : , : , :
55instantiation65, 66, 84  ⊢  
  : , : , :
56instantiation92, 81, 67  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
58instantiation92, 68, 69  ⊢  
  : , : , :
59instantiation92, 81, 70  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
61theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
62instantiation92, 71, 72  ⊢  
  : , : , :
63instantiation73, 90, 74  ⊢  
  : , :
64instantiation92, 89, 75  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
66instantiation76, 77  ⊢  
  : , :
67instantiation92, 89, 78  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
69instantiation92, 79, 80  ⊢  
  : , : , :
70instantiation92, 89, 86  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
72instantiation92, 81, 82  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
74instantiation92, 83, 84  ⊢  
  : , : , :
75instantiation85, 90  ⊢  
  :
76theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
78instantiation85, 86  ⊢  
  :
79theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
80instantiation92, 87, 88  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
82instantiation92, 89, 90  ⊢  
  : , : , :
83theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
84axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
85theorem  ⊢  
 proveit.numbers.negation.int_closure
86instantiation92, 93, 91  ⊢  
  : , : , :
87theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
88theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
89theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
90instantiation92, 93, 94  ⊢  
  : , : , :
91theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
92theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
93theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
94theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements