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