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