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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	16, 6	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	modus ponens	7, 8	⊢
6	instantiation	9, 77, 10	⊢
	: , :
7	instantiation	11, 98	⊢
	: , : , : , : , : , : , :
8	generalization	12	⊢
9	modus ponens	13, 14	⊢
10	instantiation	119, 54, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
12	instantiation	16, 17	,  ⊢
	: , :
13	instantiation	18, 111, 98, 76	⊢
	: , : , : , : , : , :
14	generalization	19	⊢
15	instantiation	31, 37, 20, 21	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	instantiation	22, 30, 23, 40, 24*	,  ⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
19	instantiation	119, 54, 25	,  ⊢
	: , : , :
20	instantiation	119, 64, 26	⊢
	: , : , :
21	instantiation	78, 49	⊢
	:
22	theorem		⊢
	proveit.numbers.division.prod_of_fracs
23	instantiation	119, 27, 28	⊢
	: , : , :
24	instantiation	29, 30	⊢
	:
25	instantiation	31, 37, 32, 33	,  ⊢
	: , :
26	instantiation	119, 71, 34	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
28	instantiation	119, 35, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
30	instantiation	119, 54, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.div_real_closure
32	instantiation	38, 55, 121	,  ⊢
	: , :
33	instantiation	39, 40	,  ⊢
	:
34	instantiation	119, 120, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
36	instantiation	119, 42, 43	⊢
	: , : , :
37	instantiation	119, 64, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
40	instantiation	45, 46, 47	,  ⊢
	: , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43	instantiation	119, 48, 49	⊢
	: , : , :
44	instantiation	119, 71, 108	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
46	instantiation	50, 51, 52	,  ⊢
	:
47	instantiation	119, 54, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
51	instantiation	119, 54, 55	,  ⊢
	: , : , :
52	instantiation	56, 57	,  ⊢
	: , :
53	instantiation	119, 64, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	59, 60, 61	,  ⊢
	: , :
56	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
57	instantiation	62, 63	,  ⊢
	: , :
58	instantiation	119, 71, 118	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
60	instantiation	119, 64, 65	,  ⊢
	: , : , :
61	instantiation	66, 67	⊢
	:
62	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
63	instantiation	68, 69, 85, 70	,  ⊢
	: , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	119, 71, 85	,  ⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.real_closure
67	instantiation	72, 73, 74	⊢
	: , :
68	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
69	instantiation	75, 76, 111, 77	⊢
	: , : , : , : , :
70	instantiation	78, 79	,  ⊢
	:
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
73	instantiation	80, 81, 82	⊢
	: , : , :
74	instantiation	83, 84	⊢
	:
75	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
76	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
77	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
78	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
79	instantiation	99, 85, 86	,  ⊢
	:
80	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
81	instantiation	87, 88	⊢
	: , :
82	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
83	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
84	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
85	instantiation	119, 89, 95	,  ⊢
	: , : , :
86	instantiation	103, 90, 91	,  ⊢
	: , : , :
87	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
89	instantiation	106, 94, 113	⊢
	: , :
90	instantiation	92, 93	⊢
	:
91	instantiation	107, 94, 113, 95	,  ⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
93	instantiation	96, 97, 98	⊢
	: , :
94	instantiation	112, 100, 108	⊢
	: , :
95	assumption		⊢
96	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
97	instantiation	99, 100, 101	⊢
	:
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
99	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
100	instantiation	119, 102, 110	⊢
	: , : , :
101	instantiation	103, 104, 105	⊢
	: , : , :
102	instantiation	106, 108, 109	⊢
	: , :
103	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
104	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
105	instantiation	107, 108, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
107	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
108	instantiation	119, 120, 111	⊢
	: , : , :
109	instantiation	112, 113, 114	⊢
	: , :
110	assumption		⊢
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
112	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
113	instantiation	119, 115, 116	⊢
	: , : , :
114	instantiation	117, 118	⊢
	:
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
116	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
117	theorem		⊢
	proveit.numbers.negation.int_closure
118	instantiation	119, 120, 121	⊢
	: , : , :
119	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements