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, 7, 8	⊢
	: , : , : , :
1	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
2	reference	20	⊢
3	instantiation	71	⊢
	: , :
4	reference	14	⊢
5	reference	23	⊢
6	instantiation	71	⊢
	: , :
7	instantiation	9, 14, 10, 11	⊢
	: , : , : , :
8	modus ponens	12, 13	⊢
9	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
10	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
11	instantiation	22, 14, 15, 16	⊢
	: , : , : , :
12	instantiation	17, 18, 23	⊢
	: , : , : , : , : , :
13	generalization	19	⊢
14	instantiation	28, 20	⊢
	:
15	instantiation	30, 31, 21	⊢
	: , :
16	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
17	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
19	instantiation	22, 23, 24, 25	,  ⊢
	: , : , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
21	instantiation	50, 26, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
23	instantiation	28, 29	⊢
	:
24	instantiation	30, 31, 32	,  ⊢
	: , :
25	instantiation	33, 99, 85	,  ⊢
	: , :
26	instantiation	68, 53, 34	⊢
	: , :
27	instantiation	46, 35, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
29	instantiation	37, 97, 94	⊢
	: , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
31	instantiation	100, 75, 38	⊢
	: , : , :
32	instantiation	50, 39, 40	,  ⊢
	: , : , :
33	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
34	instantiation	50, 41, 42	⊢
	: , : , :
35	instantiation	59, 102, 54, 60, 43, 61, 53, 69, 70, 49	⊢
	: , : , : , : , : , :
36	instantiation	59, 60, 97, 54, 61, 55, 43, 64, 65, 69, 70, 49	⊢
	: , : , : , : , : , :
37	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
38	instantiation	100, 80, 44	⊢
	: , : , :
39	instantiation	68, 53, 45	,  ⊢
	: , :
40	instantiation	46, 47, 48	,  ⊢
	: , : , :
41	instantiation	68, 58, 49	⊢
	: , :
42	instantiation	59, 60, 97, 102, 61, 62, 69, 70, 49	⊢
	: , : , : , : , : , :
43	instantiation	66	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
45	instantiation	50, 51, 52	,  ⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	59, 102, 54, 60, 56, 61, 53, 69, 70, 63	,  ⊢
	: , : , : , : , : , :
48	instantiation	59, 60, 97, 54, 61, 55, 56, 64, 65, 69, 70, 63	,  ⊢
	: , : , : , : , : , :
49	instantiation	100, 75, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.equality.sub_right_side_into
51	instantiation	68, 58, 63	,  ⊢
	: , :
52	instantiation	59, 60, 97, 102, 61, 62, 69, 70, 63	,  ⊢
	: , : , : , : , : , :
53	instantiation	68, 64, 65	⊢
	: , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
55	instantiation	71	⊢
	: , :
56	instantiation	66	⊢
	: , : , :
57	instantiation	100, 78, 67	⊢
	: , : , :
58	instantiation	68, 69, 70	⊢
	: , :
59	theorem		⊢
	proveit.numbers.multiplication.disassociation
60	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
61	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
62	instantiation	71	⊢
	: , :
63	instantiation	100, 75, 72	,  ⊢
	: , : , :
64	instantiation	100, 75, 73	⊢
	: , : , :
65	instantiation	100, 75, 74	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
67	instantiation	100, 83, 90	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
70	instantiation	100, 75, 76	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
72	instantiation	100, 78, 77	,  ⊢
	: , : , :
73	instantiation	100, 78, 79	⊢
	: , : , :
74	instantiation	100, 80, 81	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
76	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
77	instantiation	100, 83, 82	,  ⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	100, 83, 93	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
82	instantiation	100, 84, 85	,  ⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
84	instantiation	86, 87, 88	⊢
	: , :
85	assumption		⊢
86	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
87	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
88	instantiation	89, 90, 91	⊢
	: , :
89	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
90	instantiation	92, 93, 94	⊢
	: , :
91	instantiation	95, 96	⊢
	:
92	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
93	instantiation	100, 101, 97	⊢
	: , : , :
94	instantiation	100, 98, 99	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	100, 101, 102	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
98	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
99	assumption		⊢
100	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat1