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	⊢
	: , : , :
1	reference	61	⊢
2	instantiation	3, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
4	instantiation	7, 10, 151, 101, 102, 12	⊢
	: , : , : , : , : , :
5	instantiation	8, 151, 10, 12	⊢
	: , : , : , : , :
6	instantiation	9, 123, 10, 11, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
8	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
9	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
10	instantiation	31, 13, 14, 15	⊢
	: , :
11	instantiation	116	⊢
	: , :
12	instantiation	16, 17, 18, 19	⊢
	: , : , : , :
13	instantiation	149, 124, 20	⊢
	: , : , :
14	instantiation	57, 105, 21	⊢
	: , :
15	instantiation	22, 23, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
17	instantiation	25, 56	⊢
	:
18	instantiation	26, 56, 27	⊢
	: , : , :
19	modus ponens	28, 29	⊢
20	instantiation	149, 127, 30	⊢
	: , : , :
21	instantiation	31, 64, 105, 42	⊢
	: , :
22	theorem		⊢
	proveit.logic.equality.sub_left_side_into
23	instantiation	32, 94, 33	⊢
	: , :
24	instantiation	61, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
26	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
27	instantiation	83, 35, 36	⊢
	: , : , :
28	instantiation	37, 121, 47	⊢
	: , : , : , : , : , :
29	generalization	38	⊢
30	instantiation	149, 132, 145	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.div_complex_closure
32	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
33	instantiation	149, 39, 40	⊢
	: , : , :
34	instantiation	41, 64, 105, 42, 43*	⊢
	: , :
35	instantiation	44, 56	⊢
	:
36	instantiation	45, 148	⊢
	:
37	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
38	instantiation	46, 47, 48, 49	⊢
	: , : , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
40	instantiation	50, 98, 51	⊢
	: , :
41	theorem		⊢
	proveit.numbers.division.div_as_mult
42	instantiation	52, 123	⊢
	:
43	instantiation	77, 53, 54	⊢
	: , : , :
44	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
45	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
46	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
47	instantiation	55, 56	⊢
	:
48	instantiation	57, 58, 59	⊢
	: , :
49	instantiation	60, 148, 134	⊢
	: , :
50	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
51	instantiation	149, 122, 148	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
53	instantiation	61, 62	⊢
	: , : , :
54	instantiation	63, 64, 65	⊢
	: , :
55	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
56	instantiation	66, 146, 143	⊢
	: , :
57	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
58	instantiation	149, 124, 67	⊢
	: , : , :
59	instantiation	86, 68, 69	⊢
	: , : , :
60	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
61	axiom		⊢
	proveit.logic.equality.substitution
62	instantiation	70, 71, 121, 72*	⊢
	: , :
63	theorem		⊢
	proveit.numbers.multiplication.commutation
64	instantiation	149, 124, 73	⊢
	: , : , :
65	instantiation	149, 124, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
67	instantiation	149, 129, 75	⊢
	: , : , :
68	instantiation	113, 89, 76	⊢
	: , :
69	instantiation	77, 78, 79	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
71	instantiation	149, 80, 81	⊢
	: , : , :
72	instantiation	82, 105	⊢
	:
73	instantiation	83, 84, 148	⊢
	: , : , :
74	instantiation	149, 127, 85	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
76	instantiation	86, 87, 88	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.equals_transitivity
78	instantiation	100, 151, 90, 101, 92, 102, 89, 114, 115, 104	⊢
	: , : , : , : , : , :
79	instantiation	100, 101, 146, 90, 102, 91, 92, 105, 106, 114, 115, 104	⊢
	: , : , : , : , : , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
81	instantiation	149, 93, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
83	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
84	instantiation	95, 96	⊢
	: , :
85	instantiation	149, 97, 98	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.equality.sub_right_side_into
87	instantiation	113, 99, 104	⊢
	: , :
88	instantiation	100, 101, 146, 151, 102, 103, 114, 115, 104	⊢
	: , : , : , : , : , :
89	instantiation	113, 105, 106	⊢
	: , :
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
91	instantiation	116	⊢
	: , :
92	instantiation	107	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
94	instantiation	149, 108, 109	⊢
	: , : , :
95	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
98	instantiation	110, 111, 112	⊢
	: , :
99	instantiation	113, 114, 115	⊢
	: , :
100	theorem		⊢
	proveit.numbers.multiplication.disassociation
101	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
102	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
103	instantiation	116	⊢
	: , :
104	instantiation	149, 124, 117	⊢
	: , : , :
105	instantiation	149, 124, 118	⊢
	: , : , :
106	instantiation	149, 124, 119	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
109	instantiation	149, 120, 123	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
111	instantiation	149, 122, 121	⊢
	: , : , :
112	instantiation	149, 122, 123	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
115	instantiation	149, 124, 125	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
117	instantiation	149, 127, 126	⊢
	: , : , :
118	instantiation	149, 127, 128	⊢
	: , : , :
119	instantiation	149, 129, 130	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
121	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
123	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
124	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
125	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
126	instantiation	149, 132, 131	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
128	instantiation	149, 132, 142	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
131	instantiation	149, 133, 134	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
133	instantiation	135, 136, 137	⊢
	: , :
134	assumption		⊢
135	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
136	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
137	instantiation	138, 139, 140	⊢
	: , :
138	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
139	instantiation	141, 142, 143	⊢
	: , :
140	instantiation	144, 145	⊢
	:
141	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
142	instantiation	149, 150, 146	⊢
	: , : , :
143	instantiation	149, 147, 148	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.negation.int_closure
145	instantiation	149, 150, 151	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
147	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
148	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
149	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
151	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements