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