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