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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, 4, 5, 6, 7*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_product
2reference24  ⊢  
3instantiation54, 31, 8  ⊢  
  : , : , :
4instantiation9, 10  ⊢  
  :
5instantiation11, 44  ⊢  
  :
6instantiation11, 12  ⊢  
  :
7instantiation13, 14, 15, 16*  ⊢  
  : , :
8instantiation54, 38, 17  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.negation.real_closure
10instantiation54, 38, 18  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
12instantiation19, 25, 20  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
14instantiation54, 21, 22  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
16instantiation23, 24  ⊢  
  :
17instantiation54, 45, 25  ⊢  
  : , : , :
18instantiation54, 45, 41  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
20instantiation26, 27, 28  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22instantiation54, 29, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
24instantiation54, 31, 32  ⊢  
  : , : , :
25instantiation54, 33, 35  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
27theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
28instantiation34, 41, 42, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30instantiation54, 36, 37  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation54, 38, 39  ⊢  
  : , : , :
33instantiation40, 41, 42  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
35assumption  ⊢  
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37instantiation54, 43, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation54, 45, 53  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
41instantiation54, 55, 46  ⊢  
  : , : , :
42instantiation47, 48, 49  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
47theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
48instantiation54, 50, 51  ⊢  
  : , : , :
49instantiation52, 53  ⊢  
  :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
51theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53instantiation54, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements