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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,  ⊢  
  : , : , :
1reference84  ⊢  
2reference19  ⊢  
3instantiation4, 5, 6, 7,  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_real_closure
5instantiation84, 29, 8  ⊢  
  : , : , :
6instantiation9, 20, 86,  ⊢  
  : , :
7instantiation10, 11,  ⊢  
  :
8instantiation84, 36, 73  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
10theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
11instantiation12, 13, 14,  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
13instantiation15, 16, 17,  ⊢  
  :
14instantiation84, 19, 18  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
16instantiation84, 19, 20,  ⊢  
  : , : , :
17instantiation21, 22,  ⊢  
  : , :
18instantiation84, 29, 23  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
20instantiation24, 25, 26,  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
22instantiation27, 28,  ⊢  
  : , :
23instantiation84, 36, 83  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
25instantiation84, 29, 30,  ⊢  
  : , : , :
26instantiation31, 32  ⊢  
  :
27theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
28instantiation33, 34, 50, 35,  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
30instantiation84, 36, 50,  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.negation.real_closure
32instantiation37, 38, 39  ⊢  
  : , :
33theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
34instantiation40, 41, 76, 42  ⊢  
  : , : , : , : , :
35instantiation43, 44,  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
37theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
38instantiation45, 46, 47  ⊢  
  : , : , :
39instantiation48, 49  ⊢  
  :
40theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
41axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
42theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
43theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
44instantiation64, 50, 51,  ⊢  
  :
45theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
46instantiation52, 53  ⊢  
  : , :
47theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
48theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
49theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
50instantiation84, 54, 60,  ⊢  
  : , : , :
51instantiation68, 55, 56,  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54instantiation71, 59, 78  ⊢  
  : , :
55instantiation57, 58  ⊢  
  :
56instantiation72, 59, 78, 60,  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
58instantiation61, 62, 63  ⊢  
  : , :
59instantiation77, 65, 73  ⊢  
  : , :
60assumption  ⊢  
61theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
62instantiation64, 65, 66  ⊢  
  :
63theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
64theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
65instantiation84, 67, 75  ⊢  
  : , : , :
66instantiation68, 69, 70  ⊢  
  : , : , :
67instantiation71, 73, 74  ⊢  
  : , :
68theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
69theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
70instantiation72, 73, 74, 75  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
72theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
73instantiation84, 85, 76  ⊢  
  : , : , :
74instantiation77, 78, 79  ⊢  
  : , :
75assumption  ⊢  
76theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
77theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
78instantiation84, 80, 81  ⊢  
  : , : , :
79instantiation82, 83  ⊢  
  :
80theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
81theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
82theorem  ⊢  
 proveit.numbers.negation.int_closure
83instantiation84, 85, 86  ⊢  
  : , : , :
84theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
86theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2