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, 5, 6, 7, 8, 9	,  ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.disassociation
2	reference	146	⊢
3	reference	153	⊢
4	reference	65	⊢
5	instantiation	133	⊢
	: , :
6	reference	66	⊢
7	instantiation	151, 141, 10	⊢
	: , : , :
8	reference	136	⊢
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