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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  ⊢  
  : , : , :
1reference8  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation8, 6, 7  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation8, 9, 10  ⊢  
  : , : , :
6instantiation14, 17, 59, 66, 19, 11, 20, 30, 34  ⊢  
  : , : , : , : , : , :
7instantiation12, 30, 20, 13  ⊢  
  : , : , :
8axiom  ⊢  
 proveit.logic.equality.equals_transitivity
9instantiation14, 17, 59, 66, 19, 15, 20, 34, 33  ⊢  
  : , : , : , : , : , :
10instantiation16, 66, 59, 17, 18, 19, 20, 34, 33, 21*  ⊢  
  : , : , : , : , : , :
11instantiation23  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
13instantiation22  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.addition.disassociation
15instantiation23  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.addition.association
17axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
18instantiation23  ⊢  
  : , :
19theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20instantiation64, 38, 24  ⊢  
  : , : , :
21instantiation25, 26, 27  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
23theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24instantiation64, 52, 28  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
26instantiation29, 30, 33, 31  ⊢  
  : , : , :
27instantiation32, 33, 34  ⊢  
  : , :
28instantiation64, 35, 36  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add
30instantiation64, 38, 45  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
32theorem  ⊢  
 proveit.numbers.addition.commutation
33instantiation64, 38, 37  ⊢  
  : , : , :
34instantiation64, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
36instantiation40, 41, 42  ⊢  
  : , :
37instantiation64, 52, 43  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation44, 45  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_nonzero_closure
41instantiation64, 46, 47  ⊢  
  : , : , :
42instantiation48, 49, 50  ⊢  
  : , :
43instantiation64, 60, 51  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.negation.real_closure
45instantiation64, 52, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
47instantiation64, 54, 55  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
49instantiation64, 62, 56  ⊢  
  : , : , :
50instantiation57, 58  ⊢  
  :
51instantiation64, 65, 59  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation64, 60, 61  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
55theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
56axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
57theorem  ⊢  
 proveit.numbers.negation.int_closure
58instantiation64, 62, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
60theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
61instantiation64, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
63axiom  ⊢  
 proveit.physics.quantum.QPE._n_in_natural_pos
64theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements