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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation8, 9, 4  ⊢  
  : , :
3instantiation5, 6, 7  ⊢  
  : , : , :
4instantiation8, 17, 18  ⊢  
  : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation10, 64, 44, 11, 14, 12, 9, 17, 18  ⊢  
  : , : , : , : , : , :
7instantiation10, 11, 44, 12, 13, 14, 15, 16, 17, 18  ⊢  
  : , : , : , : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
9instantiation65, 41, 19  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
12theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13instantiation20  ⊢  
  : , :
14instantiation20  ⊢  
  : , :
15instantiation65, 41, 25  ⊢  
  : , : , :
16instantiation65, 41, 26  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
18instantiation21, 22, 23  ⊢  
  : , :
19instantiation24, 25, 26  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
22instantiation65, 41, 27  ⊢  
  : , : , :
23instantiation28, 29  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
25instantiation65, 45, 30  ⊢  
  : , : , :
26instantiation65, 31, 32  ⊢  
  : , : , :
27instantiation33, 34  ⊢  
  :
28theorem  ⊢  
 proveit.numbers.negation.complex_closure
29instantiation35, 36, 37, 38  ⊢  
  : , :
30instantiation65, 50, 39  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
33theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
34theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
35theorem  ⊢  
 proveit.numbers.division.div_complex_closure
36instantiation65, 41, 40  ⊢  
  : , : , :
37instantiation65, 41, 42  ⊢  
  : , : , :
38instantiation43, 49  ⊢  
  :
39instantiation65, 63, 44  ⊢  
  : , : , :
40instantiation65, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
42instantiation47, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation65, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
48instantiation52, 53  ⊢  
  : , :
49theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation65, 54, 55  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54instantiation56, 57, 62  ⊢  
  : , :
55assumption  ⊢  
56theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
57instantiation58, 59, 60  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
59instantiation61, 62  ⊢  
  :
60instantiation65, 63, 64  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.negation.int_closure
62instantiation65, 66, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
64theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
65theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
66theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
67theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos