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