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, 4, 5*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.division.div_as_mult
2	instantiation	78, 6, 7	⊢
	: , : , :
3	instantiation	174, 152, 17	⊢
	: , : , :
4	instantiation	8, 173, 13, 97, 9	⊢
	: , :
5	instantiation	126, 10, 11	⊢
	: , : , :
6	instantiation	174, 152, 12	⊢
	: , : , :
7	instantiation	70, 72, 173, 171, 73, 13, 146, 109, 53	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
9	instantiation	174, 111, 90	⊢
	: , : , :
10	instantiation	137, 14	⊢
	: , : , :
11	instantiation	126, 15, 16	⊢
	: , : , :
12	instantiation	116, 17, 65	⊢
	: , :
13	instantiation	94	⊢
	: , :
14	instantiation	18, 146, 109, 85, 60, 67, 19*	⊢
	: , : , :
15	instantiation	126, 20, 21	⊢
	: , : , :
16	instantiation	126, 22, 23	⊢
	: , : , :
17	instantiation	116, 153, 122	⊢
	: , :
18	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
19	instantiation	24, 97, 144, 25*	⊢
	: , :
20	instantiation	126, 26, 27	⊢
	: , : , :
21	instantiation	126, 28, 29	⊢
	: , : , :
22	instantiation	71, 72, 44, 73, 46, 109, 53, 52	⊢
	: , : , : , :
23	instantiation	126, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
25	instantiation	91, 146	⊢
	:
26	instantiation	70, 72, 44, 171, 73, 34, 146, 109, 53, 32	⊢
	: , : , : , : , : , :
27	instantiation	70, 44, 173, 72, 34, 33, 73, 146, 109, 53, 47, 52	⊢
	: , : , : , : , : , :
28	instantiation	49, 72, 44, 171, 73, 34, 146, 109, 53, 47, 52	⊢
	: , : , : , : , : , : , :
29	instantiation	126, 35, 36	⊢
	: , : , :
30	instantiation	126, 37, 38	⊢
	: , : , :
31	instantiation	39, 171, 72, 73, 120, 55, 40, 41*, 42*	⊢
	: , : , : , : , : , :
32	instantiation	43, 47, 52	⊢
	: , :
33	instantiation	94	⊢
	: , :
34	instantiation	58	⊢
	: , : , :
35	instantiation	50, 72, 173, 44, 73, 45, 46, 47, 146, 109, 53, 52	⊢
	: , : , : , : , : , :
36	instantiation	137, 48	⊢
	: , : , :
37	instantiation	49, 171, 72, 73, 109, 53, 52	⊢
	: , : , : , : , : , : , :
38	instantiation	50, 72, 173, 171, 73, 51, 109, 52, 53, 54*	⊢
	: , : , : , : , : , :
39	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
40	instantiation	174, 152, 105	⊢
	: , : , :
41	instantiation	136, 55	⊢
	:
42	instantiation	126, 56, 57	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
45	instantiation	94	⊢
	: , :
46	instantiation	58	⊢
	: , : , :
47	instantiation	59, 120, 146, 60	⊢
	: , :
48	instantiation	78, 61, 62	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
50	theorem		⊢
	proveit.numbers.multiplication.association
51	instantiation	94	⊢
	: , :
52	instantiation	63, 109, 64	⊢
	: , :
53	instantiation	174, 152, 65	⊢
	: , : , :
54	instantiation	66, 109, 131, 85, 67, 68*, 69*	⊢
	: , : , :
55	instantiation	174, 152, 87	⊢
	: , : , :
56	instantiation	70, 171, 173, 72, 74, 73, 120, 75, 76	⊢
	: , : , : , : , : , :
57	instantiation	71, 72, 173, 73, 74, 75, 76	⊢
	: , : , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
59	theorem		⊢
	proveit.numbers.division.div_complex_closure
60	instantiation	77, 165	⊢
	:
61	instantiation	78, 79, 80	⊢
	: , : , :
62	instantiation	81, 82, 83, 84	⊢
	: , : , : , :
63	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
64	instantiation	174, 152, 85	⊢
	: , : , :
65	instantiation	86, 87, 88	⊢
	: , :
66	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
67	instantiation	89, 90	⊢
	:
68	instantiation	91, 109	⊢
	:
69	instantiation	126, 92, 93	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.multiplication.disassociation
71	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
72	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
73	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
74	instantiation	94	⊢
	: , :
75	instantiation	174, 152, 117	⊢
	: , : , :
76	instantiation	174, 152, 118	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
78	theorem		⊢
	proveit.logic.equality.sub_right_side_into
79	instantiation	95, 120, 96, 97	⊢
	: , : , : , : , :
80	instantiation	126, 98, 99	⊢
	: , : , :
81	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
82	instantiation	137, 100	⊢
	: , : , :
83	instantiation	137, 100	⊢
	: , : , :
84	instantiation	145, 120	⊢
	:
85	instantiation	174, 159, 101	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
87	instantiation	102, 103	⊢
	:
88	instantiation	104, 105	⊢
	:
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
90	instantiation	174, 106, 134	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
92	instantiation	137, 107	⊢
	: , : , :
93	instantiation	108, 109	⊢
	:
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
95	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
96	instantiation	174, 111, 110	⊢
	: , : , :
97	instantiation	174, 111, 112	⊢
	: , : , :
98	instantiation	137, 113	⊢
	: , : , :
99	instantiation	137, 114	⊢
	: , : , :
100	instantiation	139, 120	⊢
	:
101	instantiation	174, 167, 115	⊢
	: , : , :
102	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
103	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
104	theorem		⊢
	proveit.numbers.negation.real_closure
105	instantiation	116, 117, 118	⊢
	: , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
107	instantiation	119, 120, 121	⊢
	: , :
108	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
109	instantiation	174, 152, 122	⊢
	: , : , :
110	instantiation	174, 124, 123	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
112	instantiation	174, 124, 150	⊢
	: , : , :
113	instantiation	137, 125	⊢
	: , : , :
114	instantiation	126, 127, 128	⊢
	: , : , :
115	instantiation	169, 163	⊢
	:
116	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
117	instantiation	174, 159, 129	⊢
	: , : , :
118	instantiation	174, 159, 130	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
120	instantiation	174, 152, 131	⊢
	: , : , :
121	instantiation	132	⊢
	:
122	instantiation	174, 133, 134	⊢
	: , : , :
123	instantiation	174, 156, 135	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
125	instantiation	136, 146	⊢
	:
126	axiom		⊢
	proveit.logic.equality.equals_transitivity
127	instantiation	137, 138	⊢
	: , : , :
128	instantiation	139, 146	⊢
	:
129	instantiation	174, 167, 140	⊢
	: , : , :
130	instantiation	174, 141, 142	⊢
	: , : , :
131	instantiation	174, 159, 143	⊢
	: , : , :
132	axiom		⊢
	proveit.logic.equality.equals_reflexivity
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
134	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
135	instantiation	174, 164, 144	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
137	axiom		⊢
	proveit.logic.equality.substitution
138	instantiation	145, 146	⊢
	:
139	theorem		⊢
	proveit.numbers.division.frac_one_denom
140	instantiation	174, 147, 148	⊢
	: , : , :
141	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
142	instantiation	149, 150, 151	⊢
	: , :
143	instantiation	174, 167, 163	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
145	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
146	instantiation	174, 152, 153	⊢
	: , : , :
147	instantiation	154, 155, 170	⊢
	: , :
148	assumption		⊢
149	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
150	instantiation	174, 156, 157	⊢
	: , : , :
151	instantiation	169, 158	⊢
	:
152	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
153	instantiation	174, 159, 160	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
155	instantiation	161, 162, 163	⊢
	: , :
156	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
157	instantiation	174, 164, 165	⊢
	: , : , :
158	instantiation	174, 175, 166	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
160	instantiation	174, 167, 168	⊢
	: , : , :
161	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
162	instantiation	169, 170	⊢
	:
163	instantiation	174, 172, 171	⊢
	: , : , :
164	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
165	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
166	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
167	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
168	instantiation	174, 172, 173	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.negation.int_closure
170	instantiation	174, 175, 176	⊢
	: , : , :
171	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
172	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
173	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
174	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
175	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
176	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements