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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,  ⊢  
  : , :
1reference7  ⊢  
2instantiation14, 3, 4, 5,  ⊢  
  : , : , : , :
3instantiation18, 33, 35  ⊢  
  : , :
4instantiation6  ⊢  
  :
5instantiation7, 8,  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
7theorem  ⊢  
 proveit.logic.equality.equals_reversal
8instantiation9, 10, 11,  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation12, 13,  ⊢  
  : , : , :
11instantiation14, 15, 16, 17,  ⊢  
  : , : , : , :
12axiom  ⊢  
 proveit.logic.equality.substitution
13instantiation18, 33, 28,  ⊢  
  : , :
14theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
15instantiation20, 25, 71, 64, 26, 21, 27, 23, 19,  ⊢  
  : , : , : , : , : , :
16instantiation20, 71, 25, 21, 22, 26, 27, 23, 28, 29,  ⊢  
  : , : , : , : , : , :
17instantiation24, 64, 25, 26, 27, 28, 29,  ⊢  
  : , : , : , : , : , : , : , :
18theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
19instantiation69, 40, 30  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.addition.disassociation
21instantiation31  ⊢  
  : , :
22instantiation31  ⊢  
  : , :
23instantiation69, 40, 32  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general_rev
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27instantiation34, 33  ⊢  
  :
28instantiation69, 40, 38  ⊢  
  : , : , :
29instantiation34, 35  ⊢  
  :
30instantiation36, 38, 37  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32instantiation41, 38  ⊢  
  :
33instantiation69, 40, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.negation.complex_closure
35instantiation69, 40, 42  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
37instantiation41, 42  ⊢  
  :
38instantiation69, 45, 43  ⊢  
  : , : , :
39instantiation69, 45, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41theorem  ⊢  
 proveit.numbers.negation.real_closure
42instantiation69, 45, 46  ⊢  
  : , : , :
43instantiation69, 49, 47  ⊢  
  : , : , :
44instantiation69, 49, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation69, 49, 60  ⊢  
  : , : , :
47instantiation69, 50, 51  ⊢  
  : , : , :
48instantiation69, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
50instantiation57, 54, 63  ⊢  
  : , :
51instantiation55, 56  ⊢  
  : , :
52instantiation57, 60, 58  ⊢  
  : , :
53assumption  ⊢  
54instantiation61, 59, 60  ⊢  
  : , :
55theorem  ⊢  
 proveit.logic.booleans.conjunction.left_from_and
56assumption  ⊢  
57theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
58instantiation61, 63, 62  ⊢  
  : , :
59instantiation65, 63  ⊢  
  :
60instantiation69, 70, 64  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
62instantiation65, 66  ⊢  
  :
63instantiation69, 67, 68  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
65theorem  ⊢  
 proveit.numbers.negation.int_closure
66instantiation69, 70, 71  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
68theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
69theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2