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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.numbers.absolute_value.complex_unit_length
2instantiation4, 5, 6  ⊢  
  : , : , :
3instantiation7, 8  ⊢  
  : , :
4theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
5instantiation13, 9, 33  ⊢  
  : , :
6instantiation10, 21, 47, 63, 23, 18, 25, 26, 27  ⊢  
  : , : , : , : , : , :
7theorem  ⊢  
 proveit.logic.equality.equals_reversal
8instantiation11, 12  ⊢  
  : , : , :
9instantiation13, 30, 31  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11axiom  ⊢  
 proveit.logic.equality.substitution
12instantiation14, 15, 16  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation17, 21, 47, 63, 23, 18, 25, 26, 24, 27  ⊢  
  : , : , : , : , : , : , :
16instantiation19, 63, 20, 21, 22, 23, 24, 25, 26, 27  ⊢  
  : , : , : , : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
18instantiation28  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.multiplication.association
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22instantiation29  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
25instantiation64, 32, 30  ⊢  
  : , : , :
26instantiation64, 32, 31  ⊢  
  : , : , :
27instantiation64, 32, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
30instantiation64, 49, 34  ⊢  
  : , : , :
31instantiation64, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation37, 38, 39  ⊢  
  : , :
34instantiation64, 51, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
37theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
38instantiation41, 42, 43, 44  ⊢  
  : , : , :
39instantiation45, 46  ⊢  
  :
40instantiation64, 62, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
43instantiation64, 49, 48  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
45theorem  ⊢  
 proveit.numbers.negation.real_closure
46instantiation64, 49, 50  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
48instantiation64, 51, 59  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
50instantiation64, 51, 52  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
52instantiation64, 53, 54  ⊢  
  : , : , :
53instantiation55, 56, 61  ⊢  
  : , :
54assumption  ⊢  
55theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
56instantiation57, 58, 59  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
58instantiation60, 61  ⊢  
  :
59instantiation64, 62, 63  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.negation.int_closure
61instantiation64, 65, 66  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
63theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
64theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
66theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements