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	reference	37	⊢
2	modus ponens	6, 7	⊢
3	instantiation	22, 135	⊢
	: , :
4	instantiation	22, 135	⊢
	: , :
5	instantiation	8, 9, 10, 11	⊢
	: , : , : , :
6	instantiation	30, 46	⊢
	: , : , : , : , : , : , :
7	generalization	12	⊢
8	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
9	instantiation	37, 13, 14*, 15*	⊢
	: , : , :
10	instantiation	59, 16	⊢
	: , :
11	instantiation	37, 17	⊢
	: , : , :
12	instantiation	101, 18, 19	,  ⊢
	: , : , :
13	modus ponens	20, 21	⊢
14	instantiation	22, 135	⊢
	: , :
15	instantiation	22, 135	⊢
	: , :
16	modus ponens	23, 24	⊢
17	instantiation	59, 25	⊢
	: , :
18	instantiation	55, 26, 27	,  ⊢
	: , : , :
19	instantiation	97, 28, 29	,  ⊢
	: , : , :
20	instantiation	30, 46	⊢
	: , : , : , : , : , : , :
21	generalization	31	⊢
22	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
23	instantiation	32, 46, 64, 43	⊢
	: , : , : , : , : , : , : , :
24	modus ponens	33, 34	⊢
25	modus ponens	35, 36	⊢
26	instantiation	37, 38	,  ⊢
	: , : , :
27	instantiation	39, 95, 82, 54	,  ⊢
	: , : , :
28	instantiation	59, 40	,  ⊢
	: , :
29	instantiation	41, 149, 135	,  ⊢
	: , :
30	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
31	instantiation	42, 67, 43	,  ⊢
	: , :
32	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
33	instantiation	44, 46, 64	⊢
	: , : , : , : , : , :
34	generalization	56	⊢
35	instantiation	45, 152, 46, 111, 64, 112	⊢
	: , : , : , : , : , : , : , : , : , : , :
36	generalization	47	⊢
37	axiom		⊢
	proveit.logic.equality.substitution
38	instantiation	48, 49, 147, 111, 50, 51, 112, 115, 116, 119, 120, 114, 93	,  ⊢
	: , : , : , : , : , :
39	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
40	instantiation	52, 53	,  ⊢
	: , : , :
41	theorem		⊢
	proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket
42	theorem		⊢
	proveit.numbers.multiplication.commutation
43	instantiation	80, 81, 54	⊢
	: , :
44	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
45	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	instantiation	55, 56, 57	,  ⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
50	instantiation	58	⊢
	: , : , : , :
51	instantiation	121	⊢
	: , :
52	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_eq
53	instantiation	59, 60	,  ⊢
	: , :
54	instantiation	101, 61, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.equality.sub_left_side_into
56	instantiation	63, 64, 67, 65	,  ⊢
	: , : , : , :
57	instantiation	66, 67, 152, 111, 112, 75, 76, 78, 79	,  ⊢
	: , : , : , : , : , : , : , : , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
59	theorem		⊢
	proveit.logic.equality.equals_reversal
60	instantiation	68, 114, 93	,  ⊢
	: , :
61	instantiation	118, 104, 69	⊢
	: , :
62	instantiation	97, 70, 71	⊢
	: , : , :
63	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
64	instantiation	72, 86, 74, 75, 76	⊢
	: , : , :
65	instantiation	73, 86, 74, 75, 76, 77, 78, 79	,  ⊢
	: , : , : , :
66	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
67	instantiation	80, 81, 82	,  ⊢
	: , :
68	theorem		⊢
	proveit.numbers.addition.commutation
69	instantiation	101, 83, 84	⊢
	: , : , :
70	instantiation	110, 152, 105, 111, 85, 112, 104, 119, 120, 93	⊢
	: , : , : , : , : , :
71	instantiation	110, 111, 147, 105, 112, 106, 85, 115, 116, 119, 120, 93	⊢
	: , : , : , : , : , :
72	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
73	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
74	instantiation	121	⊢
	: , :
75	instantiation	87, 86	⊢
	:
76	instantiation	87, 88	⊢
	:
77	instantiation	121	⊢
	: , :
78	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
79	instantiation	89, 149, 135	,  ⊢
	: , :
80	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
81	instantiation	150, 125, 90	⊢
	: , : , :
82	instantiation	101, 91, 92	,  ⊢
	: , : , :
83	instantiation	118, 109, 93	⊢
	: , :
84	instantiation	110, 111, 147, 152, 112, 113, 119, 120, 93	⊢
	: , : , : , : , : , :
85	instantiation	117	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
87	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
88	instantiation	94, 147, 144	⊢
	: , :
89	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
90	instantiation	150, 130, 95	⊢
	: , : , :
91	instantiation	118, 104, 96	,  ⊢
	: , :
92	instantiation	97, 98, 99	,  ⊢
	: , : , :
93	instantiation	150, 125, 100	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
96	instantiation	101, 102, 103	,  ⊢
	: , : , :
97	axiom		⊢
	proveit.logic.equality.equals_transitivity
98	instantiation	110, 152, 105, 111, 107, 112, 104, 119, 120, 114	,  ⊢
	: , : , : , : , : , :
99	instantiation	110, 111, 147, 105, 112, 106, 107, 115, 116, 119, 120, 114	,  ⊢
	: , : , : , : , : , :
100	instantiation	150, 128, 108	⊢
	: , : , :
101	theorem		⊢
	proveit.logic.equality.sub_right_side_into
102	instantiation	118, 109, 114	,  ⊢
	: , :
103	instantiation	110, 111, 147, 152, 112, 113, 119, 120, 114	,  ⊢
	: , : , : , : , : , :
104	instantiation	118, 115, 116	⊢
	: , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
106	instantiation	121	⊢
	: , :
107	instantiation	117	⊢
	: , : , :
108	instantiation	150, 133, 140	⊢
	: , : , :
109	instantiation	118, 119, 120	⊢
	: , :
110	theorem		⊢
	proveit.numbers.multiplication.disassociation
111	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
112	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
113	instantiation	121	⊢
	: , :
114	instantiation	150, 125, 122	,  ⊢
	: , : , :
115	instantiation	150, 125, 123	⊢
	: , : , :
116	instantiation	150, 125, 124	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
118	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
120	instantiation	150, 125, 126	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
122	instantiation	150, 128, 127	,  ⊢
	: , : , :
123	instantiation	150, 128, 129	⊢
	: , : , :
124	instantiation	150, 130, 131	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
126	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
127	instantiation	150, 133, 132	,  ⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
129	instantiation	150, 133, 143	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
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