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