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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, 5, 6,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
2theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
3instantiation7  ⊢  
  : , : , :
4instantiation100, 16, 8  ⊢  
  : , : , :
5instantiation100, 16, 9  ⊢  
  : , : , :
6instantiation10, 11, 12,  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8instantiation100, 14, 13  ⊢  
  : , : , :
9instantiation100, 14, 15  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
11instantiation100, 16, 17,  ⊢  
  : , : , :
12instantiation29, 18  ⊢  
  : , : , :
13instantiation100, 20, 19  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
15instantiation100, 20, 21  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
17instantiation100, 22, 23,  ⊢  
  : , : , :
18instantiation29, 24  ⊢  
  : , : , :
19instantiation100, 26, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
21instantiation100, 26, 55  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
23instantiation27, 28,  ⊢  
  :
24instantiation29, 30  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
26theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
27theorem  ⊢  
 proveit.numbers.absolute_value.abs_nonzero_closure
28instantiation31, 32, 33,  ⊢  
  :
29axiom  ⊢  
 proveit.logic.equality.substitution
30instantiation34, 35, 36, 37, 38*  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
32instantiation100, 76, 39  ⊢  
  : , : , :
33instantiation40, 41,  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.division.div_as_mult
35instantiation100, 76, 42  ⊢  
  : , : , :
36instantiation100, 76, 43  ⊢  
  : , : , :
37instantiation81, 55  ⊢  
  :
38instantiation44, 45, 77, 46, 73, 47*  ⊢  
  : , : , :
39instantiation48, 49, 61, 50  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
41instantiation51, 52, 66, 53,  ⊢  
  : , :
42instantiation100, 79, 54  ⊢  
  : , : , :
43instantiation85, 86, 55  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
45instantiation100, 76, 72  ⊢  
  : , : , :
46instantiation100, 79, 56  ⊢  
  : , : , :
47instantiation57, 69, 58, 59*  ⊢  
  : , :
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
49instantiation60, 61  ⊢  
  :
50instantiation62, 75  ⊢  
  :
51theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_not_eq_scaledNonzeroInt
52instantiation63, 64, 99, 65  ⊢  
  : , : , : , : , :
53assumption  ⊢  
54instantiation100, 88, 66  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
56instantiation100, 88, 67  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
58instantiation100, 76, 71  ⊢  
  : , : , :
59instantiation68, 69  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.negation.real_closure
61instantiation70, 71, 72, 73  ⊢  
  : , :
62theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
63theorem  ⊢  
 proveit.logic.sets.enumeration.in_enumerated_set
64axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
65theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
66instantiation100, 74, 75  ⊢  
  : , : , :
67instantiation96, 92  ⊢  
  :
68theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
69instantiation100, 76, 77  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.division.div_real_closure
71instantiation100, 79, 78  ⊢  
  : , : , :
72instantiation100, 79, 80  ⊢  
  : , : , :
73instantiation81, 82  ⊢  
  :
74instantiation83, 84, 97  ⊢  
  : , :
75assumption  ⊢  
76theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
77instantiation85, 86, 87  ⊢  
  : , : , :
78instantiation100, 88, 92  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
80instantiation100, 88, 89  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
82theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
83theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
84instantiation90, 91, 92  ⊢  
  : , :
85theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
86instantiation93, 94  ⊢  
  : , :
87axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
88theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
89instantiation100, 98, 95  ⊢  
  : , : , :
90theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
91instantiation96, 97  ⊢  
  :
92instantiation100, 98, 99  ⊢  
  : , : , :
93theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
94theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
95theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
96theorem  ⊢  
 proveit.numbers.negation.int_closure
97instantiation100, 101, 102  ⊢  
  : , : , :
98theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
99theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
100theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
101theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
102theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements