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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  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 37, 30, 10, 11, 12, 13*  ⊢  
  : , : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation14, 73, 83, 16, 18, 17, 41, 19, 20  ⊢  
  : , : , : , : , : , :
8instantiation15, 16, 83, 17, 18, 19, 20  ⊢  
  : , : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_product
10instantiation21, 52  ⊢  
  :
11instantiation22, 66  ⊢  
  :
12instantiation22, 23  ⊢  
  :
13instantiation24, 25, 64, 26*  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.multiplication.disassociation
15theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
16axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
17theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18instantiation27  ⊢  
  : , :
19instantiation81, 51, 28  ⊢  
  : , : , :
20instantiation29, 30, 31  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.negation.real_closure
22theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
23instantiation32, 60, 33  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
25instantiation81, 34, 35  ⊢  
  : , : , :
26instantiation36, 37  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28instantiation81, 61, 38  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
30instantiation81, 51, 39  ⊢  
  : , : , :
31instantiation40, 41  ⊢  
  :
32theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
33instantiation42, 43, 44  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
35instantiation81, 45, 46  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
37instantiation81, 51, 47  ⊢  
  : , : , :
38instantiation81, 48, 49  ⊢  
  : , : , :
39instantiation81, 61, 50  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.negation.complex_closure
41instantiation81, 51, 52  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
43theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
44instantiation53, 71, 72, 68  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
46instantiation81, 54, 55  ⊢  
  : , : , :
47instantiation81, 61, 56  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49instantiation57, 58, 59  ⊢  
  : , :
50instantiation81, 69, 60  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52instantiation81, 61, 62  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
55instantiation81, 63, 66  ⊢  
  : , : , :
56instantiation81, 69, 80  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
58instantiation81, 65, 64  ⊢  
  : , : , :
59instantiation81, 65, 66  ⊢  
  : , : , :
60instantiation81, 67, 68  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
62instantiation81, 69, 71  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
64theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
65theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
66theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
67instantiation70, 71, 72  ⊢  
  : , :
68assumption  ⊢  
69theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
70theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
71instantiation81, 82, 73  ⊢  
  : , : , :
72instantiation74, 75, 76  ⊢  
  : , :
73theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
74theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
75instantiation81, 77, 78  ⊢  
  : , : , :
76instantiation79, 80  ⊢  
  :
77theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
78theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
79theorem  ⊢  
 proveit.numbers.negation.int_closure
80instantiation81, 82, 83  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
83theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements