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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,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5,  ⊢  
  : , : , :
3instantiation6, 7, 8, 9,  ⊢  
  : , : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation10, 25, 20,  ⊢  
  : , :
6theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
7instantiation12, 17, 63, 56, 18, 13, 19, 15, 11,  ⊢  
  : , : , : , : , : , :
8instantiation12, 63, 17, 13, 14, 18, 19, 15, 20, 21,  ⊢  
  : , : , : , : , : , :
9instantiation16, 56, 17, 18, 19, 20, 21,  ⊢  
  : , : , : , : , : , : , : , :
10theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
11instantiation61, 32, 22  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.addition.disassociation
13instantiation23  ⊢  
  : , :
14instantiation23  ⊢  
  : , :
15instantiation61, 32, 24  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general_rev
17axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
18theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19instantiation26, 25  ⊢  
  :
20instantiation61, 32, 30  ⊢  
  : , : , :
21instantiation26, 27  ⊢  
  :
22instantiation28, 30, 29  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24instantiation33, 30  ⊢  
  :
25instantiation61, 32, 31  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.negation.complex_closure
27instantiation61, 32, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
29instantiation33, 34  ⊢  
  :
30instantiation61, 37, 35  ⊢  
  : , : , :
31instantiation61, 37, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33theorem  ⊢  
 proveit.numbers.negation.real_closure
34instantiation61, 37, 38  ⊢  
  : , : , :
35instantiation61, 41, 39  ⊢  
  : , : , :
36instantiation61, 41, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation61, 41, 52  ⊢  
  : , : , :
39instantiation61, 42, 43  ⊢  
  : , : , :
40instantiation61, 44, 45  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation49, 46, 55  ⊢  
  : , :
43instantiation47, 48  ⊢  
  : , :
44instantiation49, 52, 50  ⊢  
  : , :
45assumption  ⊢  
46instantiation53, 51, 52  ⊢  
  : , :
47theorem  ⊢  
 proveit.logic.booleans.conjunction.left_from_and
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
50instantiation53, 55, 54  ⊢  
  : , :
51instantiation57, 55  ⊢  
  :
52instantiation61, 62, 56  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
54instantiation57, 58  ⊢  
  :
55instantiation61, 59, 60  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
57theorem  ⊢  
 proveit.numbers.negation.int_closure
58instantiation61, 62, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
60theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
61theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2