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