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, 80, 12	⊢
	: , :
9	instantiation	13, 108	⊢
	: , : , : , : , : , : , :
10	generalization	14	⊢
11	modus ponens	15, 16	⊢
12	instantiation	129, 57, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
14	instantiation	18, 19	,  ⊢
	: , :
15	instantiation	20, 121, 108, 79	⊢
	: , : , : , : , : , :
16	generalization	21	⊢
17	instantiation	34, 40, 22, 23	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.equals_reversal
19	instantiation	24, 33, 25, 43, 26*	,  ⊢
	: , : , : , :
20	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
21	instantiation	129, 57, 27	,  ⊢
	: , : , :
22	instantiation	129, 67, 28	⊢
	: , : , :
23	instantiation	29, 52	⊢
	:
24	theorem		⊢
	proveit.numbers.division.prod_of_fracs
25	instantiation	129, 30, 31	⊢
	: , : , :
26	instantiation	32, 33	⊢
	:
27	instantiation	34, 40, 35, 36	,  ⊢
	: , :
28	instantiation	129, 74, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
31	instantiation	129, 38, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
33	instantiation	129, 57, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.division.div_real_closure
35	instantiation	41, 58, 131	,  ⊢
	: , :
36	instantiation	42, 43	,  ⊢
	:
37	instantiation	129, 130, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
39	instantiation	129, 45, 46	⊢
	: , : , :
40	instantiation	129, 67, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
43	instantiation	48, 49, 50	,  ⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46	instantiation	129, 51, 52	⊢
	: , : , :
47	instantiation	129, 74, 118	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
49	instantiation	53, 54, 55	,  ⊢
	:
50	instantiation	129, 57, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
54	instantiation	129, 57, 58	,  ⊢
	: , : , :
55	instantiation	59, 60	,  ⊢
	: , :
56	instantiation	129, 67, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	62, 63, 64	,  ⊢
	: , :
59	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
60	instantiation	65, 66	,  ⊢
	: , :
61	instantiation	129, 74, 128	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
63	instantiation	129, 67, 68	,  ⊢
	: , : , :
64	instantiation	69, 70	⊢
	:
65	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
66	instantiation	71, 72, 82, 73	,  ⊢
	: , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	129, 74, 82	,  ⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.negation.real_closure
70	instantiation	75, 76, 77	⊢
	: , :
71	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
72	instantiation	78, 79, 121, 80	⊢
	: , : , : , : , :
73	instantiation	81, 82, 83, 84	,  ⊢
	: , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
76	instantiation	85, 86, 87	⊢
	: , : , :
77	instantiation	88, 89	⊢
	:
78	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
79	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
80	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
81	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
82	instantiation	129, 90, 99	,  ⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
84	instantiation	91, 92, 93	,  ⊢
	: , : , :
85	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
86	instantiation	94, 95	⊢
	: , :
87	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
88	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
89	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
90	instantiation	116, 97, 98	⊢
	: , :
91	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
92	instantiation	96, 97, 98, 99	,  ⊢
	: , : , :
93	instantiation	100, 101	⊢
	:
94	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
96	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
97	instantiation	122, 102, 118	⊢
	: , :
98	instantiation	127, 103	⊢
	:
99	assumption		⊢
100	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
101	instantiation	104, 105	⊢
	:
102	instantiation	127, 123	⊢
	:
103	instantiation	122, 110, 118	⊢
	: , :
104	theorem		⊢
	proveit.numbers.negation.int_neg_closure
105	instantiation	106, 107, 108	⊢
	: , :
106	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
107	instantiation	109, 110, 111	⊢
	:
108	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
109	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
110	instantiation	129, 112, 120	⊢
	: , : , :
111	instantiation	113, 114, 115	⊢
	: , : , :
112	instantiation	116, 118, 119	⊢
	: , :
113	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
114	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
115	instantiation	117, 118, 119, 120	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
117	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
118	instantiation	129, 130, 121	⊢
	: , : , :
119	instantiation	122, 123, 124	⊢
	: , :
120	assumption		⊢
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
122	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
123	instantiation	129, 125, 126	⊢
	: , : , :
124	instantiation	127, 128	⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
126	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
127	theorem		⊢
	proveit.numbers.negation.int_closure
128	instantiation	129, 130, 131	⊢
	: , : , :
129	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements