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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_shift
2instantiation61, 50, 56  ⊢  
  : , :
3reference62  ⊢  
4reference54  ⊢  
5instantiation14, 7, 8  ⊢  
  : , : , :
6instantiation14, 9, 10,  ⊢  
  : , : , :
7instantiation24, 25, 72, 60, 26, 11, 12, 40, 28  ⊢  
  : , : , : , : , : , :
8instantiation29, 40, 12, 31  ⊢  
  : , : , :
9instantiation33, 13  ⊢  
  : , : , :
10instantiation14, 15, 16,  ⊢  
  : , : , :
11instantiation35  ⊢  
  : , :
12instantiation70, 42, 17  ⊢  
  : , : , :
13instantiation18, 19, 20, 21, 22, 23  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation24, 25, 72, 60, 26, 27, 30, 40, 28,  ⊢  
  : , : , : , : , : , :
16instantiation29, 40, 30, 31,  ⊢  
  : , : , :
17instantiation70, 45, 32  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
19theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
20instantiation35  ⊢  
  : , :
21instantiation35  ⊢  
  : , :
22instantiation33, 34  ⊢  
  : , : , :
23instantiation38  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.addition.disassociation
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27instantiation35  ⊢  
  : , :
28instantiation36, 40  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
30instantiation70, 42, 37,  ⊢  
  : , : , :
31instantiation38  ⊢  
  :
32instantiation70, 49, 50  ⊢  
  : , : , :
33axiom  ⊢  
 proveit.logic.equality.substitution
34instantiation39, 40  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36theorem  ⊢  
 proveit.numbers.negation.complex_closure
37instantiation70, 45, 41,  ⊢  
  : , : , :
38axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
39theorem  ⊢  
 proveit.numbers.negation.double_negation
40instantiation70, 42, 43  ⊢  
  : , : , :
41instantiation70, 49, 44,  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation70, 45, 46  ⊢  
  : , : , :
44instantiation70, 47, 48,  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation70, 49, 56  ⊢  
  : , : , :
47instantiation55, 50, 51  ⊢  
  : , :
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
50instantiation70, 52, 53  ⊢  
  : , : , :
51instantiation61, 62, 54  ⊢  
  : , :
52instantiation55, 56, 57  ⊢  
  : , :
53assumption  ⊢  
54instantiation70, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
56instantiation70, 71, 60  ⊢  
  : , : , :
57instantiation61, 62, 63  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
59instantiation64, 65  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
61theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
62instantiation70, 66, 67  ⊢  
  : , : , :
63instantiation68, 69  ⊢  
  :
64theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
65theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
67theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
68theorem  ⊢  
 proveit.numbers.negation.int_closure
69instantiation70, 71, 72  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
72theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements