| step type | requirements | statement |
0 | instantiation | 1, 2, 3 | , ⊢ |
| : , : , : |
1 | reference | 138 | ⊢ |
2 | reference | 128 | ⊢ |
3 | instantiation | 10, 30, 106, 4 | , ⊢ |
| : , : , : |
4 | instantiation | 5, 6 | , ⊢ |
| : |
5 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
6 | instantiation | 7, 30, 90, 8, 9 | , ⊢ |
| : , : , : |
7 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
8 | instantiation | 10, 30, 21, 19 | , ⊢ |
| : , : , : |
9 | instantiation | 11, 12, 13 | , ⊢ |
| : , : |
10 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
11 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
12 | instantiation | 14, 30, 21, 19 | , ⊢ |
| : , : , : |
13 | instantiation | 15, 16, 17 | , ⊢ |
| : , : , : |
14 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
15 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
16 | instantiation | 18, 30, 21, 19 | , ⊢ |
| : , : , : |
17 | instantiation | 20, 21, 22, 59, 23, 24*, 25* | ⊢ |
| : , : , : |
18 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
19 | instantiation | 26, 27, 28 | , ⊢ |
| : |
20 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
21 | instantiation | 105, 90, 129, 107 | ⊢ |
| : , : |
22 | instantiation | 64, 65, 30 | ⊢ |
| : , : |
23 | instantiation | 29, 65, 30, 90, 31, 32 | ⊢ |
| : , : , : |
24 | instantiation | 33, 34, 35, 36 | ⊢ |
| : , : , : , : |
25 | instantiation | 95, 37, 38 | ⊢ |
| : , : , : |
26 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval |
27 | assumption | | ⊢ |
28 | assumption | | ⊢ |
29 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
30 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
31 | instantiation | 39, 104 | ⊢ |
| : |
32 | instantiation | 40, 79 | ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
34 | instantiation | 95, 41, 42 | ⊢ |
| : , : , : |
35 | instantiation | 43 | ⊢ |
| : |
36 | instantiation | 44, 58 | ⊢ |
| : , : |
37 | instantiation | 73, 58 | ⊢ |
| : , : , : |
38 | instantiation | 44, 45, 46* | ⊢ |
| : , : |
39 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
40 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
41 | instantiation | 95, 47, 48 | ⊢ |
| : , : , : |
42 | instantiation | 49, 50 | ⊢ |
| : |
43 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
44 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
45 | instantiation | 51, 52, 140, 133, 53, 54, 77, 76 | ⊢ |
| : , : , : , : , : , : |
46 | instantiation | 95, 55, 56 | ⊢ |
| : , : , : |
47 | instantiation | 73, 57 | ⊢ |
| : , : , : |
48 | instantiation | 73, 58 | ⊢ |
| : , : , : |
49 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
50 | instantiation | 138, 128, 59 | ⊢ |
| : , : , : |
51 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
52 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
53 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
54 | instantiation | 120 | ⊢ |
| : , : |
55 | instantiation | 73, 60 | ⊢ |
| : , : , : |
56 | instantiation | 121, 76 | ⊢ |
| : |
57 | instantiation | 61, 77 | ⊢ |
| : |
58 | instantiation | 62, 76, 123, 107, 63* | ⊢ |
| : , : |
59 | instantiation | 64, 65, 90 | ⊢ |
| : , : |
60 | instantiation | 66, 127, 137, 67* | ⊢ |
| : , : , : , : |
61 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
62 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
63 | instantiation | 95, 68, 69 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
65 | instantiation | 138, 134, 70 | ⊢ |
| : , : , : |
66 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
67 | instantiation | 95, 71, 72 | ⊢ |
| : , : , : |
68 | instantiation | 73, 74 | ⊢ |
| : , : , : |
69 | instantiation | 75, 76, 77 | ⊢ |
| : , : |
70 | instantiation | 138, 78, 79 | ⊢ |
| : , : , : |
71 | instantiation | 110, 140, 80, 81, 82, 83 | ⊢ |
| : , : , : , : |
72 | instantiation | 84, 85, 86 | ⊢ |
| : |
73 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
74 | instantiation | 87, 88, 108, 89* | ⊢ |
| : , : |
75 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
76 | instantiation | 138, 128, 90 | ⊢ |
| : , : , : |
77 | instantiation | 138, 128, 91 | ⊢ |
| : , : , : |
78 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
79 | instantiation | 92, 93, 94 | ⊢ |
| : , : |
80 | instantiation | 120 | ⊢ |
| : , : |
81 | instantiation | 120 | ⊢ |
| : , : |
82 | instantiation | 95, 96, 97 | ⊢ |
| : , : , : |
83 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
84 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
85 | instantiation | 138, 128, 98 | ⊢ |
| : , : , : |
86 | instantiation | 119, 99 | ⊢ |
| : |
87 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
88 | instantiation | 138, 100, 101 | ⊢ |
| : , : , : |
89 | instantiation | 102, 123 | ⊢ |
| : |
90 | instantiation | 138, 103, 104 | ⊢ |
| : , : , : |
91 | instantiation | 105, 106, 129, 107 | ⊢ |
| : , : |
92 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
93 | instantiation | 138, 109, 108 | ⊢ |
| : , : , : |
94 | instantiation | 138, 109, 132 | ⊢ |
| : , : , : |
95 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
96 | instantiation | 110, 140, 111, 112, 113, 114 | ⊢ |
| : , : , : , : |
97 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
98 | instantiation | 138, 134, 115 | ⊢ |
| : , : , : |
99 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
100 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
101 | instantiation | 138, 116, 117 | ⊢ |
| : , : , : |
102 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
103 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
104 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
105 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
106 | instantiation | 138, 134, 118 | ⊢ |
| : , : , : |
107 | instantiation | 119, 132 | ⊢ |
| : |
108 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
109 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
110 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
111 | instantiation | 120 | ⊢ |
| : , : |
112 | instantiation | 120 | ⊢ |
| : , : |
113 | instantiation | 121, 123 | ⊢ |
| : |
114 | instantiation | 122, 123 | ⊢ |
| : |
115 | instantiation | 138, 136, 124 | ⊢ |
| : , : , : |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
117 | instantiation | 138, 125, 126 | ⊢ |
| : , : , : |
118 | instantiation | 138, 136, 127 | ⊢ |
| : , : , : |
119 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
120 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
121 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
122 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
123 | instantiation | 138, 128, 129 | ⊢ |
| : , : , : |
124 | instantiation | 138, 139, 130 | ⊢ |
| : , : , : |
125 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
126 | instantiation | 138, 131, 132 | ⊢ |
| : , : , : |
127 | instantiation | 138, 139, 133 | ⊢ |
| : , : , : |
128 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
129 | instantiation | 138, 134, 135 | ⊢ |
| : , : , : |
130 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
131 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
132 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
134 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
135 | instantiation | 138, 136, 137 | ⊢ |
| : , : , : |
136 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
137 | instantiation | 138, 139, 140 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
139 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
140 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |