Show the Proof

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

	step type	requirements	statement
0	instantiation	1, 2	,  ⊢
	: , :
1	reference	45	⊢
2	instantiation	3, 4, 5, 6, 7	,  ⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.division.strong_div_from_denom_bound__all_pos
4	instantiation	136, 9, 8	⊢
	: , : , :
5	instantiation	136, 9, 10	,  ⊢
	: , : , :
6	instantiation	11, 28, 12	,  ⊢
	:
7	instantiation	13, 102, 14, 28, 15, 16	,  ⊢
	: , : , :
8	instantiation	136, 17, 72	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
10	instantiation	136, 17, 18	,  ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
12	instantiation	19, 20	,  ⊢
	: , :
13	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_less
14	instantiation	35, 36, 40	,  ⊢
	: , :
15	instantiation	21, 34, 22	,  ⊢
	: , :
16	instantiation	23, 24	⊢
	:
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
18	instantiation	25, 26, 138	,  ⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	27, 84, 28, 29	,  ⊢
	: , :
21	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
22	instantiation	30, 36, 40, 37, 31	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
25	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
26	instantiation	32, 33, 34	,  ⊢
	:
27	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
28	instantiation	35, 36, 37	,  ⊢
	: , :
29	instantiation	60, 38	,  ⊢
	: , :
30	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
31	instantiation	39, 40, 48, 119, 50, 41, 42*, 43*	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
33	instantiation	126, 62, 44	,  ⊢
	: , :
34	instantiation	45, 46	,  ⊢
	: , :
35	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
36	instantiation	136, 124, 47	,  ⊢
	: , : , :
37	instantiation	51, 48	⊢
	:
38	instantiation	49, 50, 61	,  ⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound
40	instantiation	51, 119	⊢
	:
41	instantiation	52, 59	⊢
	:
42	instantiation	53, 110, 54*	⊢
	: , :
43	instantiation	55, 56, 57	⊢
	: , : , :
44	instantiation	136, 58, 59	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.ordering.relax_less
46	instantiation	60, 61	,  ⊢
	: , :
47	instantiation	136, 129, 62	,  ⊢
	: , : , :
48	instantiation	63, 84, 119, 65	⊢
	: , : , :
49	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
50	instantiation	64, 84, 119, 65	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.negation.real_closure
52	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
53	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
54	instantiation	66, 110	⊢
	:
55	axiom		⊢
	proveit.logic.equality.equals_transitivity
56	instantiation	67, 135, 138, 78, 80, 79, 68, 81, 82	⊢
	: , : , : , : , : , :
57	instantiation	69, 78, 138, 79, 80, 110, 81, 82, 70*	⊢
	: , : , : , : , :
58	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
59	instantiation	71, 72	⊢
	:
60	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
61	instantiation	96, 73, 74	,  ⊢
	: , : , :
62	instantiation	136, 75, 88	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
65	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
66	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
67	theorem		⊢
	proveit.numbers.multiplication.disassociation
68	instantiation	76, 110	⊢
	:
69	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
70	instantiation	77, 78, 138, 79, 80, 81, 82	⊢
	: , : , : , :
71	theorem		⊢
	proveit.numbers.negation.int_neg_closure
72	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
73	instantiation	83, 119, 84, 85, 86, 87*	⊢
	: , : , :
74	instantiation	107, 89, 127, 88	,  ⊢
	: , : , :
75	instantiation	122, 89, 127	⊢
	: , :
76	theorem		⊢
	proveit.numbers.negation.complex_closure
77	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
78	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
79	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
80	instantiation	90	⊢
	: , :
81	instantiation	91, 92, 93	⊢
	: , :
82	instantiation	136, 118, 94	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
85	instantiation	136, 124, 95	⊢
	: , : , :
86	instantiation	96, 97, 98	⊢
	: , : , :
87	instantiation	99, 100, 101	⊢
	: , : , :
88	assumption		⊢
89	instantiation	126, 106, 130	⊢
	: , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
91	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
92	instantiation	136, 118, 102	⊢
	: , : , :
93	instantiation	136, 118, 103	⊢
	: , : , :
94	instantiation	104, 105	⊢
	:
95	instantiation	136, 129, 106	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
97	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
98	instantiation	107, 130, 123, 117	⊢
	: , : , :
99	theorem		⊢
	proveit.logic.equality.sub_right_side_into
100	instantiation	108, 110	⊢
	:
101	instantiation	109, 110, 111	⊢
	: , :
102	instantiation	136, 124, 112	⊢
	: , : , :
103	instantiation	113, 114, 115	⊢
	: , : , :
104	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
105	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
106	instantiation	136, 116, 117	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
108	theorem		⊢
	proveit.numbers.addition.elim_zero_right
109	theorem		⊢
	proveit.numbers.addition.commutation
110	instantiation	136, 118, 119	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
112	instantiation	136, 129, 134	⊢
	: , : , :
113	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
114	instantiation	120, 121	⊢
	: , :
115	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
116	instantiation	122, 130, 123	⊢
	: , :
117	assumption		⊢
118	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
119	instantiation	136, 124, 125	⊢
	: , : , :
120	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
122	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
123	instantiation	126, 127, 128	⊢
	: , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
125	instantiation	136, 129, 130	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
127	instantiation	136, 131, 132	⊢
	: , : , :
128	instantiation	133, 134	⊢
	:
129	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
130	instantiation	136, 137, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
132	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
133	theorem		⊢
	proveit.numbers.negation.int_closure
134	instantiation	136, 137, 138	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
136	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
137	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements