| step type | requirements | statement |
0 | instantiation | 1, 2, 3, 4, 5, 6, 7, 8, 9 | , ⊢ |
| : , : , : , : , : , : |
1 | theorem | | ⊢ |
| proveit.numbers.multiplication.disassociation |
2 | reference | 65 | ⊢ |
3 | reference | 153 | ⊢ |
4 | reference | 146 | ⊢ |
5 | reference | 66 | ⊢ |
6 | instantiation | 133 | ⊢ |
| : , : |
7 | reference | 136 | ⊢ |
8 | instantiation | 151, 141, 10 | ⊢ |
| : , : , : |
9 | instantiation | 151, 141, 11 | , ⊢ |
| : , : , : |
10 | instantiation | 12, 13, 14 | ⊢ |
| : , : , : |
11 | instantiation | 23, 43, 119, 15 | , ⊢ |
| : , : , : |
12 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.unfold_subset_eq |
13 | instantiation | 16, 17 | ⊢ |
| : , : |
14 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._two_pow_t_is_nat_pos |
15 | instantiation | 18, 19 | , ⊢ |
| : |
16 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.relax_proper_subset |
17 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
18 | theorem | | ⊢ |
| proveit.trigonometry.sine_pos_interval |
19 | instantiation | 20, 43, 103, 21, 22 | , ⊢ |
| : , : , : |
20 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.in_IntervalOO |
21 | instantiation | 23, 43, 34, 32 | , ⊢ |
| : , : , : |
22 | instantiation | 24, 25, 26 | , ⊢ |
| : , : |
23 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real |
24 | theorem | | ⊢ |
| proveit.logic.booleans.conjunction.and_if_both |
25 | instantiation | 27, 43, 34, 32 | , ⊢ |
| : , : , : |
26 | instantiation | 28, 29, 30 | , ⊢ |
| : , : , : |
27 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound |
28 | theorem | | ⊢ |
| proveit.numbers.ordering.transitivity_less_eq_less |
29 | instantiation | 31, 43, 34, 32 | , ⊢ |
| : , : , : |
30 | instantiation | 33, 34, 35, 72, 36, 37*, 38* | ⊢ |
| : , : , : |
31 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound |
32 | instantiation | 39, 40, 41 | , ⊢ |
| : |
33 | theorem | | ⊢ |
| proveit.numbers.addition.strong_bound_via_left_term_bound |
34 | instantiation | 118, 103, 142, 120 | ⊢ |
| : , : |
35 | instantiation | 77, 78, 43 | ⊢ |
| : , : |
36 | instantiation | 42, 78, 43, 103, 44, 45 | ⊢ |
| : , : , : |
37 | instantiation | 46, 47, 48, 49 | ⊢ |
| : , : , : , : |
38 | instantiation | 108, 50, 51 | ⊢ |
| : , : , : |
39 | theorem | | ⊢ |
| proveit.physics.quantum.QPE._scaled_abs_delta_b_floor_diff_interval |
40 | assumption | | ⊢ |
41 | assumption | | ⊢ |
42 | theorem | | ⊢ |
| proveit.numbers.multiplication.strong_bound_via_right_factor_bound |
43 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.zero_is_real |
44 | instantiation | 52, 117 | ⊢ |
| : |
45 | instantiation | 53, 92 | ⊢ |
| : |
46 | theorem | | ⊢ |
| proveit.logic.equality.four_chain_transitivity |
47 | instantiation | 108, 54, 55 | ⊢ |
| : , : , : |
48 | instantiation | 56 | ⊢ |
| : |
49 | instantiation | 57, 71 | ⊢ |
| : , : |
50 | instantiation | 86, 71 | ⊢ |
| : , : , : |
51 | instantiation | 57, 58, 59* | ⊢ |
| : , : |
52 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos |
53 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos |
54 | instantiation | 108, 60, 61 | ⊢ |
| : , : , : |
55 | instantiation | 62, 63 | ⊢ |
| : |
56 | axiom | | ⊢ |
| proveit.logic.equality.equals_reflexivity |
57 | theorem | | ⊢ |
| proveit.logic.equality.equals_reversal |
58 | instantiation | 64, 65, 153, 146, 66, 67, 90, 89 | ⊢ |
| : , : , : , : , : , : |
59 | instantiation | 108, 68, 69 | ⊢ |
| : , : , : |
60 | instantiation | 86, 70 | ⊢ |
| : , : , : |
61 | instantiation | 86, 71 | ⊢ |
| : , : , : |
62 | theorem | | ⊢ |
| proveit.numbers.addition.elim_zero_left |
63 | instantiation | 151, 141, 72 | ⊢ |
| : , : , : |
64 | theorem | | ⊢ |
| proveit.numbers.multiplication.distribute_through_sum |
65 | axiom | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.zero_in_nats |
66 | theorem | | ⊢ |
| proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
67 | instantiation | 133 | ⊢ |
| : , : |
68 | instantiation | 86, 73 | ⊢ |
| : , : , : |
69 | instantiation | 134, 89 | ⊢ |
| : |
70 | instantiation | 74, 90 | ⊢ |
| : |
71 | instantiation | 75, 89, 136, 120, 76* | ⊢ |
| : , : |
72 | instantiation | 77, 78, 103 | ⊢ |
| : , : |
73 | instantiation | 79, 140, 150, 80* | ⊢ |
| : , : , : , : |
74 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_zero_right |
75 | theorem | | ⊢ |
| proveit.numbers.division.div_as_mult |
76 | instantiation | 108, 81, 82 | ⊢ |
| : , : , : |
77 | theorem | | ⊢ |
| proveit.numbers.multiplication.mult_real_closure_bin |
78 | instantiation | 151, 147, 83 | ⊢ |
| : , : , : |
79 | theorem | | ⊢ |
| proveit.numbers.addition.rational_pair_addition |
80 | instantiation | 108, 84, 85 | ⊢ |
| : , : , : |
81 | instantiation | 86, 87 | ⊢ |
| : , : , : |
82 | instantiation | 88, 89, 90 | ⊢ |
| : , : |
83 | instantiation | 151, 91, 92 | ⊢ |
| : , : , : |
84 | instantiation | 123, 153, 93, 94, 95, 96 | ⊢ |
| : , : , : , : |
85 | instantiation | 97, 98, 99 | ⊢ |
| : |
86 | axiom | | ⊢ |
| proveit.logic.equality.substitution |
87 | instantiation | 100, 101, 121, 102* | ⊢ |
| : , : |
88 | theorem | | ⊢ |
| proveit.numbers.multiplication.commutation |
89 | instantiation | 151, 141, 103 | ⊢ |
| : , : , : |
90 | instantiation | 151, 141, 104 | ⊢ |
| : , : , : |
91 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
92 | instantiation | 105, 106, 107 | ⊢ |
| : , : |
93 | instantiation | 133 | ⊢ |
| : , : |
94 | instantiation | 133 | ⊢ |
| : , : |
95 | instantiation | 108, 109, 110 | ⊢ |
| : , : , : |
96 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.mult_2_2 |
97 | theorem | | ⊢ |
| proveit.numbers.division.frac_cancel_complete |
98 | instantiation | 151, 141, 111 | ⊢ |
| : , : , : |
99 | instantiation | 132, 112 | ⊢ |
| : |
100 | theorem | | ⊢ |
| proveit.numbers.exponentiation.neg_power_as_div |
101 | instantiation | 151, 113, 114 | ⊢ |
| : , : , : |
102 | instantiation | 115, 136 | ⊢ |
| : |
103 | instantiation | 151, 116, 117 | ⊢ |
| : , : , : |
104 | instantiation | 118, 119, 142, 120 | ⊢ |
| : , : |
105 | theorem | | ⊢ |
| proveit.numbers.division.div_rational_pos_closure |
106 | instantiation | 151, 122, 121 | ⊢ |
| : , : , : |
107 | instantiation | 151, 122, 145 | ⊢ |
| : , : , : |
108 | axiom | | ⊢ |
| proveit.logic.equality.equals_transitivity |
109 | instantiation | 123, 153, 124, 125, 126, 127 | ⊢ |
| : , : , : , : |
110 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.add_2_2 |
111 | instantiation | 151, 147, 128 | ⊢ |
| : , : , : |
112 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat4 |
113 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
114 | instantiation | 151, 129, 130 | ⊢ |
| : , : , : |
115 | theorem | | ⊢ |
| proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
116 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.real_pos_within_real |
117 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
118 | theorem | | ⊢ |
| proveit.numbers.division.div_real_closure |
119 | instantiation | 151, 147, 131 | ⊢ |
| : , : , : |
120 | instantiation | 132, 145 | ⊢ |
| : |
121 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat1 |
122 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
123 | axiom | | ⊢ |
| proveit.core_expr_types.operations.operands_substitution |
124 | instantiation | 133 | ⊢ |
| : , : |
125 | instantiation | 133 | ⊢ |
| : , : |
126 | instantiation | 134, 136 | ⊢ |
| : |
127 | instantiation | 135, 136 | ⊢ |
| : |
128 | instantiation | 151, 149, 137 | ⊢ |
| : , : , : |
129 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
130 | instantiation | 151, 138, 139 | ⊢ |
| : , : , : |
131 | instantiation | 151, 149, 140 | ⊢ |
| : , : , : |
132 | theorem | | ⊢ |
| proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
133 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
134 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_left |
135 | theorem | | ⊢ |
| proveit.numbers.multiplication.elim_one_right |
136 | instantiation | 151, 141, 142 | ⊢ |
| : , : , : |
137 | instantiation | 151, 152, 143 | ⊢ |
| : , : , : |
138 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
139 | instantiation | 151, 144, 145 | ⊢ |
| : , : , : |
140 | instantiation | 151, 152, 146 | ⊢ |
| : , : , : |
141 | theorem | | ⊢ |
| proveit.numbers.number_sets.complex_numbers.real_within_complex |
142 | instantiation | 151, 147, 148 | ⊢ |
| : , : , : |
143 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat4 |
144 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
145 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.posnat2 |
146 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat1 |
147 | theorem | | ⊢ |
| proveit.numbers.number_sets.real_numbers.rational_within_real |
148 | instantiation | 151, 149, 150 | ⊢ |
| : , : , : |
149 | theorem | | ⊢ |
| proveit.numbers.number_sets.rational_numbers.int_within_rational |
150 | instantiation | 151, 152, 153 | ⊢ |
| : , : , : |
151 | theorem | | ⊢ |
| proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
152 | theorem | | ⊢ |
| proveit.numbers.number_sets.integers.nat_within_int |
153 | theorem | | ⊢ |
| proveit.numbers.numerals.decimals.nat2 |
*equality replacement requirements |