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, 6, 7, 8, 9	⊢
	: , : , : , : , : , : , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
2	instantiation	29, 10, 11, 12	⊢
	: , :
3	reference	155	⊢
4	reference	98	⊢
5	reference	99	⊢
6	reference	23	⊢
7	reference	35	⊢
8	instantiation	13, 23, 14, 15	⊢
	: , : , : , :
9	modus ponens	16, 17	⊢
10	instantiation	153, 124, 18	⊢
	: , : , :
11	instantiation	47, 102, 19	⊢
	: , :
12	instantiation	20, 21, 22	⊢
	: , : , :
13	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
14	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
15	instantiation	34, 23, 24, 25	⊢
	: , : , : , :
16	instantiation	26, 132, 35	⊢
	: , : , : , : , : , :
17	generalization	27	⊢
18	instantiation	153, 127, 28	⊢
	: , : , :
19	instantiation	29, 66, 102, 41	⊢
	: , :
20	theorem		⊢
	proveit.logic.equality.sub_left_side_into
21	instantiation	30, 106, 31	⊢
	: , :
22	instantiation	63, 32	⊢
	: , : , :
23	instantiation	45, 134	⊢
	:
24	instantiation	47, 48, 33	⊢
	: , :
25	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
26	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
27	instantiation	34, 35, 36, 37	,  ⊢
	: , : , : , :
28	instantiation	153, 136, 149	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.division.div_complex_closure
30	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
31	instantiation	153, 38, 39	⊢
	: , : , :
32	instantiation	40, 66, 102, 41, 42*	⊢
	: , :
33	instantiation	82, 43, 44	⊢
	: , : , :
34	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
35	instantiation	45, 46	⊢
	:
36	instantiation	47, 48, 49	,  ⊢
	: , :
37	instantiation	50, 152, 138	,  ⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
39	instantiation	51, 110, 52	⊢
	: , :
40	theorem		⊢
	proveit.numbers.division.div_as_mult
41	instantiation	53, 134	⊢
	:
42	instantiation	73, 54, 55	⊢
	: , : , :
43	instantiation	112, 85, 56	⊢
	: , :
44	instantiation	73, 57, 58	⊢
	: , : , :
45	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
46	instantiation	59, 150, 147	⊢
	: , :
47	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
48	instantiation	153, 124, 60	⊢
	: , : , :
49	instantiation	82, 61, 62	,  ⊢
	: , : , :
50	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
51	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
52	instantiation	153, 133, 152	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
54	instantiation	63, 64	⊢
	: , : , :
55	instantiation	65, 66, 67	⊢
	: , :
56	instantiation	82, 68, 69	⊢
	: , : , :
57	instantiation	97, 155, 86, 98, 70, 99, 85, 113, 114, 81	⊢
	: , : , : , : , : , :
58	instantiation	97, 98, 150, 86, 99, 87, 70, 102, 103, 113, 114, 81	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
60	instantiation	153, 129, 71	⊢
	: , : , :
61	instantiation	112, 85, 72	,  ⊢
	: , :
62	instantiation	73, 74, 75	,  ⊢
	: , : , :
63	axiom		⊢
	proveit.logic.equality.substitution
64	instantiation	76, 77, 132, 78*	⊢
	: , :
65	theorem		⊢
	proveit.numbers.multiplication.commutation
66	instantiation	153, 124, 79	⊢
	: , : , :
67	instantiation	153, 124, 80	⊢
	: , : , :
68	instantiation	112, 96, 81	⊢
	: , :
69	instantiation	97, 98, 150, 155, 99, 100, 113, 114, 81	⊢
	: , : , : , : , : , :
70	instantiation	104	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
72	instantiation	82, 83, 84	,  ⊢
	: , : , :
73	axiom		⊢
	proveit.logic.equality.equals_transitivity
74	instantiation	97, 155, 86, 98, 88, 99, 85, 113, 114, 101	,  ⊢
	: , : , : , : , : , :
75	instantiation	97, 98, 150, 86, 99, 87, 88, 102, 103, 113, 114, 101	,  ⊢
	: , : , : , : , : , :
76	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
77	instantiation	153, 89, 90	⊢
	: , : , :
78	instantiation	91, 102	⊢
	:
79	instantiation	92, 93, 152	⊢
	: , : , :
80	instantiation	153, 127, 94	⊢
	: , : , :
81	instantiation	153, 124, 95	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.equality.sub_right_side_into
83	instantiation	112, 96, 101	,  ⊢
	: , :
84	instantiation	97, 98, 150, 155, 99, 100, 113, 114, 101	,  ⊢
	: , : , : , : , : , :
85	instantiation	112, 102, 103	⊢
	: , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
87	instantiation	115	⊢
	: , :
88	instantiation	104	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	153, 105, 106	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
92	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
93	instantiation	107, 108	⊢
	: , :
94	instantiation	153, 109, 110	⊢
	: , : , :
95	instantiation	153, 127, 111	⊢
	: , : , :
96	instantiation	112, 113, 114	⊢
	: , :
97	theorem		⊢
	proveit.numbers.multiplication.disassociation
98	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
99	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
100	instantiation	115	⊢
	: , :
101	instantiation	153, 124, 116	,  ⊢
	: , : , :
102	instantiation	153, 124, 117	⊢
	: , : , :
103	instantiation	153, 124, 118	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
106	instantiation	153, 119, 120	⊢
	: , : , :
107	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
110	instantiation	121, 122, 123	⊢
	: , :
111	instantiation	153, 136, 143	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
114	instantiation	153, 124, 125	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
116	instantiation	153, 127, 126	,  ⊢
	: , : , :
117	instantiation	153, 127, 128	⊢
	: , : , :
118	instantiation	153, 129, 130	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
120	instantiation	153, 131, 134	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
122	instantiation	153, 133, 132	⊢
	: , : , :
123	instantiation	153, 133, 134	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
125	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
126	instantiation	153, 136, 135	,  ⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
128	instantiation	153, 136, 146	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
132	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
133	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
134	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
135	instantiation	153, 137, 138	,  ⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
137	instantiation	139, 140, 141	⊢
	: , :
138	assumption		⊢
139	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
140	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
141	instantiation	142, 143, 144	⊢
	: , :
142	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
143	instantiation	145, 146, 147	⊢
	: , :
144	instantiation	148, 149	⊢
	:
145	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
146	instantiation	153, 154, 150	⊢
	: , : , :
147	instantiation	153, 151, 152	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.negation.int_closure
149	instantiation	153, 154, 155	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
151	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
152	assumption		⊢
153	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements