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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  ⊢  
  : , : , :
1reference9  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 59, 8*  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10, 11  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
7instantiation55, 12, 13  ⊢  
  : , : , :
8instantiation14, 15  ⊢  
  :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation16, 17, 52, 18, 19, 20, 23, 24, 21  ⊢  
  : , : , : , : , : , :
11instantiation22, 23, 24, 25  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
13instantiation55, 26, 27  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
15instantiation55, 31, 28  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.addition.disassociation
17axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
19theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20instantiation29  ⊢  
  : , :
21instantiation55, 31, 30  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
23instantiation55, 31, 39  ⊢  
  : , : , :
24instantiation55, 31, 32  ⊢  
  : , : , :
25instantiation33  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27instantiation55, 34, 35  ⊢  
  : , : , :
28instantiation55, 36, 37  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30instantiation38, 39  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation55, 40, 41  ⊢  
  : , : , :
33axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35instantiation55, 42, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation55, 44, 45  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.negation.real_closure
39instantiation46, 47, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
41instantiation55, 49, 50  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation55, 51, 52  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
47instantiation53, 54  ⊢  
  : , :
48axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
50instantiation55, 56, 57  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
53theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
57instantiation58, 59  ⊢  
  :
58theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
59theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements