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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*  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.numbers.summation.index_negate
2instantiation55, 30, 50  ⊢  
  : , :
3instantiation60, 41  ⊢  
  :
4instantiation18, 7  ⊢  
  :
5instantiation8, 9, 10, 11*  ⊢  
  : , :
6instantiation12, 13, 54, 14*,  ⊢  
  : , :
7instantiation62, 28, 15  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
9instantiation62, 28, 16  ⊢  
  : , : , :
10instantiation62, 28, 17  ⊢  
  : , : , :
11instantiation18, 19  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.exponentiation.even_pow_is_even_fn
13instantiation62, 28, 20,  ⊢  
  : , : , :
14instantiation21, 22  ⊢  
  :
15instantiation62, 34, 23  ⊢  
  : , : , :
16instantiation62, 34, 24  ⊢  
  : , : , :
17instantiation62, 34, 25  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.negation.double_negation
19instantiation62, 28, 26  ⊢  
  : , : , :
20instantiation62, 34, 27,  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
22instantiation62, 28, 29  ⊢  
  : , : , :
23instantiation62, 40, 41  ⊢  
  : , : , :
24instantiation62, 40, 30  ⊢  
  : , : , :
25instantiation62, 40, 50  ⊢  
  : , : , :
26instantiation31, 32, 59  ⊢  
  : , : , :
27instantiation62, 40, 33,  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation62, 34, 35  ⊢  
  : , : , :
30instantiation60, 56  ⊢  
  :
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation36, 37  ⊢  
  : , :
33instantiation62, 38, 39,  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation62, 40, 61  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
38instantiation49, 41, 42  ⊢  
  : , :
39assumption  ⊢  
40theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
41instantiation55, 43, 50  ⊢  
  : , :
42instantiation55, 56, 44  ⊢  
  : , :
43instantiation62, 45, 46  ⊢  
  : , : , :
44instantiation62, 47, 48  ⊢  
  : , : , :
45instantiation49, 50, 51  ⊢  
  : , :
46assumption  ⊢  
47theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
48instantiation52, 53  ⊢  
  :
49theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
50instantiation62, 63, 54  ⊢  
  : , : , :
51instantiation55, 56, 57  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
53theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
56instantiation62, 58, 59  ⊢  
  : , : , :
57instantiation60, 61  ⊢  
  :
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
59theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
60theorem  ⊢  
 proveit.numbers.negation.int_closure
61instantiation62, 63, 64  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
64theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements