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