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