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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, 4,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_real_closure
2reference47  ⊢  
3instantiation5, 6, 7  ⊢  
  : , :
4instantiation8, 25, 9, 10, 11,  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
6instantiation70, 55, 12  ⊢  
  : , : , :
7instantiation70, 13, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
9instantiation15  ⊢  
  : , :
10instantiation70, 17, 16  ⊢  
  : , : , :
11instantiation70, 17, 18,  ⊢  
  : , : , :
12instantiation70, 57, 19  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
14instantiation20, 33  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16instantiation70, 21, 22  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18instantiation70, 23, 24,  ⊢  
  : , : , :
19instantiation70, 68, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.absolute_value.abs_complex_closure
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
22instantiation70, 26, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
24instantiation28, 29,  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
26theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
27instantiation70, 30, 31  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
29instantiation32, 33, 34,  ⊢  
  :
30theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
31theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
33instantiation70, 35, 36  ⊢  
  : , : , :
34instantiation37, 38,  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation39, 40, 41  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
38instantiation42, 43, 58, 44,  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
40instantiation45, 46, 47, 48  ⊢  
  : , : , :
41instantiation49, 50  ⊢  
  :
42theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
43instantiation51, 52, 69, 53  ⊢  
  : , : , : , : , :
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
47instantiation70, 55, 54  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
49theorem  ⊢  
 proveit.numbers.negation.real_closure
50instantiation70, 55, 56  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
52axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
53theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
54instantiation70, 57, 65  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
56instantiation70, 57, 58  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
58instantiation70, 59, 60  ⊢  
  : , : , :
59instantiation61, 62, 67  ⊢  
  : , :
60assumption  ⊢  
61theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
62instantiation63, 64, 65  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
64instantiation66, 67  ⊢  
  :
65instantiation70, 68, 69  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.negation.int_closure
67instantiation70, 71, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
69theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
70theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
72theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos