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