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