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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
0generalization1  ⊢  
1instantiation83, 18, 2,  ⊢  
  : , : , :
2instantiation3, 4, 5, 6,  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_real_closure
4instantiation83, 28, 7  ⊢  
  : , : , :
5instantiation8, 19, 85,  ⊢  
  : , :
6instantiation9, 10,  ⊢  
  :
7instantiation83, 35, 72  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
9theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
10instantiation11, 12, 13,  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
12instantiation14, 15, 16,  ⊢  
  :
13instantiation83, 18, 17  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
15instantiation83, 18, 19,  ⊢  
  : , : , :
16instantiation20, 21,  ⊢  
  : , :
17instantiation83, 28, 22  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
19instantiation23, 24, 25,  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
21instantiation26, 27,  ⊢  
  : , :
22instantiation83, 35, 82  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
24instantiation83, 28, 29,  ⊢  
  : , : , :
25instantiation30, 31  ⊢  
  :
26theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
27instantiation32, 33, 49, 34,  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
29instantiation83, 35, 49,  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.negation.real_closure
31instantiation36, 37, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
33instantiation39, 40, 75, 41  ⊢  
  : , : , : , : , :
34instantiation42, 43,  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
37instantiation44, 45, 46  ⊢  
  : , : , :
38instantiation47, 48  ⊢  
  :
39theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
40axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
41theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43instantiation63, 49, 50,  ⊢  
  :
44theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
45instantiation51, 52  ⊢  
  : , :
46theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
47theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
48theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
49instantiation83, 53, 59,  ⊢  
  : , : , :
50instantiation67, 54, 55,  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53instantiation70, 58, 77  ⊢  
  : , :
54instantiation56, 57  ⊢  
  :
55instantiation71, 58, 77, 59,  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
57instantiation60, 61, 62  ⊢  
  : , :
58instantiation76, 64, 72  ⊢  
  : , :
59assumption  ⊢  
60theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
61instantiation63, 64, 65  ⊢  
  :
62theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
63theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
64instantiation83, 66, 74  ⊢  
  : , : , :
65instantiation67, 68, 69  ⊢  
  : , : , :
66instantiation70, 72, 73  ⊢  
  : , :
67theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
68theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
69instantiation71, 72, 73, 74  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
71theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
72instantiation83, 84, 75  ⊢  
  : , : , :
73instantiation76, 77, 78  ⊢  
  : , :
74assumption  ⊢  
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
76theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
77instantiation83, 79, 80  ⊢  
  : , : , :
78instantiation81, 82  ⊢  
  :
79theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
80theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
81theorem  ⊢  
 proveit.numbers.negation.int_closure
82instantiation83, 84, 85  ⊢  
  : , : , :
83theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
85theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2