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