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	reference	6	⊢
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 7	⊢
	: , : , :
5	instantiation	18, 8	⊢
	: , :
6	axiom		⊢
	proveit.logic.equality.substitution
7	modus ponens	9, 10	⊢
8	instantiation	11, 79, 12	⊢
	: , :
9	instantiation	13, 100	⊢
	: , : , : , : , : , : , :
10	generalization	14	⊢
11	modus ponens	15, 16	⊢
12	instantiation	121, 56, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
14	instantiation	18, 19	,  ⊢
	: , :
15	instantiation	20, 113, 100, 78	⊢
	: , : , : , : , : , :
16	generalization	21	⊢
17	instantiation	33, 39, 22, 23	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.equals_reversal
19	instantiation	24, 32, 25, 42, 26*	,  ⊢
	: , : , : , :
20	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
21	instantiation	121, 56, 27	,  ⊢
	: , : , :
22	instantiation	121, 66, 28	⊢
	: , : , :
23	instantiation	80, 51	⊢
	:
24	theorem		⊢
	proveit.numbers.division.prod_of_fracs
25	instantiation	121, 29, 30	⊢
	: , : , :
26	instantiation	31, 32	⊢
	:
27	instantiation	33, 39, 34, 35	,  ⊢
	: , :
28	instantiation	121, 73, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
30	instantiation	121, 37, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
32	instantiation	121, 56, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.division.div_real_closure
34	instantiation	40, 57, 123	,  ⊢
	: , :
35	instantiation	41, 42	,  ⊢
	:
36	instantiation	121, 122, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
38	instantiation	121, 44, 45	⊢
	: , : , :
39	instantiation	121, 66, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
42	instantiation	47, 48, 49	,  ⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
45	instantiation	121, 50, 51	⊢
	: , : , :
46	instantiation	121, 73, 110	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
48	instantiation	52, 53, 54	,  ⊢
	:
49	instantiation	121, 56, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
53	instantiation	121, 56, 57	,  ⊢
	: , : , :
54	instantiation	58, 59	,  ⊢
	: , :
55	instantiation	121, 66, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	61, 62, 63	,  ⊢
	: , :
58	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
59	instantiation	64, 65	,  ⊢
	: , :
60	instantiation	121, 73, 120	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
62	instantiation	121, 66, 67	,  ⊢
	: , : , :
63	instantiation	68, 69	⊢
	:
64	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
65	instantiation	70, 71, 87, 72	,  ⊢
	: , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	121, 73, 87	,  ⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.negation.real_closure
69	instantiation	74, 75, 76	⊢
	: , :
70	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
71	instantiation	77, 78, 113, 79	⊢
	: , : , : , : , :
72	instantiation	80, 81	,  ⊢
	:
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
75	instantiation	82, 83, 84	⊢
	: , : , :
76	instantiation	85, 86	⊢
	:
77	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
78	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
79	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
81	instantiation	101, 87, 88	,  ⊢
	:
82	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
83	instantiation	89, 90	⊢
	: , :
84	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
85	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
86	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
87	instantiation	121, 91, 97	,  ⊢
	: , : , :
88	instantiation	105, 92, 93	,  ⊢
	: , : , :
89	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
91	instantiation	108, 96, 115	⊢
	: , :
92	instantiation	94, 95	⊢
	:
93	instantiation	109, 96, 115, 97	,  ⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
95	instantiation	98, 99, 100	⊢
	: , :
96	instantiation	114, 102, 110	⊢
	: , :
97	assumption		⊢
98	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
99	instantiation	101, 102, 103	⊢
	:
100	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
101	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
102	instantiation	121, 104, 112	⊢
	: , : , :
103	instantiation	105, 106, 107	⊢
	: , : , :
104	instantiation	108, 110, 111	⊢
	: , :
105	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
106	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
107	instantiation	109, 110, 111, 112	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
109	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
110	instantiation	121, 122, 113	⊢
	: , : , :
111	instantiation	114, 115, 116	⊢
	: , :
112	assumption		⊢
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
114	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
115	instantiation	121, 117, 118	⊢
	: , : , :
116	instantiation	119, 120	⊢
	:
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
118	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
119	theorem		⊢
	proveit.numbers.negation.int_closure
120	instantiation	121, 122, 123	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements