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