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