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.numbers.ordering.relax_less
2	instantiation	3, 4, 5	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
4	instantiation	6, 16, 7, 8	⊢
	: , : , :
5	instantiation	9, 10, 11, 12, 13	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
7	instantiation	115, 105, 14	⊢
	: , : , :
8	instantiation	15, 16, 97, 60, 17, 18*, 19*, 20*	⊢
	: , : , : , :
9	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
10	instantiation	115, 21, 22	⊢
	: , : , :
11	instantiation	115, 24, 23	⊢
	: , : , :
12	instantiation	115, 24, 25	⊢
	: , : , :
13	instantiation	26, 49, 97, 27, 28, 29, 30*	⊢
	: , : , :
14	instantiation	31, 106, 32, 66	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rescale_interval_co_membership
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
17	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
18	instantiation	72, 33, 34, 35	⊢
	: , : , : , :
19	instantiation	36, 55	⊢
	:
20	instantiation	109, 55	⊢
	:
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
22	instantiation	115, 37, 117	⊢
	: , : , :
23	instantiation	115, 39, 38	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
25	instantiation	115, 39, 120	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
27	instantiation	118, 119, 41	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
29	instantiation	40, 41	⊢
	:
30	instantiation	42, 43	⊢
	:
31	theorem		⊢
	proveit.numbers.division.div_rational_closure
32	instantiation	115, 111, 44	⊢
	: , : , :
33	instantiation	45, 117, 76, 52, 46, 53, 55, 110, 56	⊢
	: , : , : , : , : , :
34	instantiation	94, 47, 48	⊢
	: , : , :
35	instantiation	101, 56	⊢
	:
36	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
41	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
42	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43	instantiation	115, 113, 49	⊢
	: , : , :
44	instantiation	115, 50, 120	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	instantiation	59	⊢
	: , :
47	instantiation	51, 52, 76, 117, 53, 54, 55, 110, 56	⊢
	: , : , : , : , : , :
48	instantiation	102, 57	⊢
	: , : , :
49	instantiation	115, 105, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
51	theorem		⊢
	proveit.numbers.multiplication.association
52	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
53	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
54	instantiation	59	⊢
	: , :
55	instantiation	115, 113, 60	⊢
	: , : , :
56	instantiation	115, 113, 61	⊢
	: , : , :
57	instantiation	69, 62, 63	⊢
	: , : , :
58	instantiation	115, 111, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
60	instantiation	65, 97, 114, 66	⊢
	: , :
61	instantiation	67, 68	⊢
	:
62	instantiation	69, 70, 71	⊢
	: , : , :
63	instantiation	72, 73, 74, 75	⊢
	: , : , : , :
64	instantiation	115, 116, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.division.div_real_closure
66	instantiation	77, 120	⊢
	:
67	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
68	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
69	theorem		⊢
	proveit.logic.equality.sub_right_side_into
70	instantiation	78, 89, 79, 80	⊢
	: , : , : , : , :
71	instantiation	94, 81, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
73	instantiation	102, 83	⊢
	: , : , :
74	instantiation	102, 83	⊢
	: , : , :
75	instantiation	109, 89	⊢
	:
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
77	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
78	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
79	instantiation	115, 85, 84	⊢
	: , : , :
80	instantiation	115, 85, 86	⊢
	: , : , :
81	instantiation	102, 87	⊢
	: , : , :
82	instantiation	102, 88	⊢
	: , : , :
83	instantiation	104, 89	⊢
	:
84	instantiation	115, 91, 90	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
86	instantiation	115, 91, 92	⊢
	: , : , :
87	instantiation	102, 93	⊢
	: , : , :
88	instantiation	94, 95, 96	⊢
	: , : , :
89	instantiation	115, 113, 97	⊢
	: , : , :
90	instantiation	115, 99, 98	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
92	instantiation	115, 99, 100	⊢
	: , : , :
93	instantiation	101, 110	⊢
	:
94	axiom		⊢
	proveit.logic.equality.equals_transitivity
95	instantiation	102, 103	⊢
	: , : , :
96	instantiation	104, 110	⊢
	:
97	instantiation	115, 105, 106	⊢
	: , : , :
98	instantiation	115, 108, 107	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
100	instantiation	115, 108, 120	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
102	axiom		⊢
	proveit.logic.equality.substitution
103	instantiation	109, 110	⊢
	:
104	theorem		⊢
	proveit.numbers.division.frac_one_denom
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
106	instantiation	115, 111, 112	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
109	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
110	instantiation	115, 113, 114	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
112	instantiation	115, 116, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
114	instantiation	118, 119, 120	⊢
	: , : , :
115	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
118	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
119	instantiation	121, 122	⊢
	: , :
120	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
121	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements