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, 3, 4	,  ⊢
	: , : , :
1	reference	10	⊢
2	reference	30	⊢
3	reference	106	⊢
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