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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
2	instantiation	4, 22, 5, 31	⊢
	: , : , :
3	instantiation	6, 22, 7, 16, 25, 8, 9, 10	⊢
	: , : , : , :
4	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
5	instantiation	73	⊢
	: , :
6	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
7	instantiation	73	⊢
	: , :
8	instantiation	73	⊢
	: , :
9	instantiation	11, 16, 12, 13	⊢
	: , : , : , :
10	modus ponens	14, 15	⊢
11	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
12	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
13	instantiation	24, 16, 17, 18	⊢
	: , : , : , :
14	instantiation	19, 20, 25	⊢
	: , : , : , : , : , :
15	generalization	21	⊢
16	instantiation	30, 22	⊢
	:
17	instantiation	32, 33, 23	⊢
	: , :
18	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
19	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
21	instantiation	24, 25, 26, 27	,  ⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
23	instantiation	52, 28, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
25	instantiation	30, 31	⊢
	:
26	instantiation	32, 33, 34	,  ⊢
	: , :
27	instantiation	35, 101, 87	,  ⊢
	: , :
28	instantiation	70, 55, 36	⊢
	: , :
29	instantiation	48, 37, 38	⊢
	: , : , :
30	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
31	instantiation	39, 99, 96	⊢
	: , :
32	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
33	instantiation	102, 77, 40	⊢
	: , : , :
34	instantiation	52, 41, 42	,  ⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
36	instantiation	52, 43, 44	⊢
	: , : , :
37	instantiation	61, 104, 56, 62, 45, 63, 55, 71, 72, 51	⊢
	: , : , : , : , : , :
38	instantiation	61, 62, 99, 56, 63, 57, 45, 66, 67, 71, 72, 51	⊢
	: , : , : , : , : , :
39	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
40	instantiation	102, 82, 46	⊢
	: , : , :
41	instantiation	70, 55, 47	,  ⊢
	: , :
42	instantiation	48, 49, 50	,  ⊢
	: , : , :
43	instantiation	70, 60, 51	⊢
	: , :
44	instantiation	61, 62, 99, 104, 63, 64, 71, 72, 51	⊢
	: , : , : , : , : , :
45	instantiation	68	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
47	instantiation	52, 53, 54	,  ⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	61, 104, 56, 62, 58, 63, 55, 71, 72, 65	,  ⊢
	: , : , : , : , : , :
50	instantiation	61, 62, 99, 56, 63, 57, 58, 66, 67, 71, 72, 65	,  ⊢
	: , : , : , : , : , :
51	instantiation	102, 77, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	70, 60, 65	,  ⊢
	: , :
54	instantiation	61, 62, 99, 104, 63, 64, 71, 72, 65	,  ⊢
	: , : , : , : , : , :
55	instantiation	70, 66, 67	⊢
	: , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
57	instantiation	73	⊢
	: , :
58	instantiation	68	⊢
	: , : , :
59	instantiation	102, 80, 69	⊢
	: , : , :
60	instantiation	70, 71, 72	⊢
	: , :
61	theorem		⊢
	proveit.numbers.multiplication.disassociation
62	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
63	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
64	instantiation	73	⊢
	: , :
65	instantiation	102, 77, 74	,  ⊢
	: , : , :
66	instantiation	102, 77, 75	⊢
	: , : , :
67	instantiation	102, 77, 76	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
69	instantiation	102, 85, 92	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
72	instantiation	102, 77, 78	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
74	instantiation	102, 80, 79	,  ⊢
	: , : , :
75	instantiation	102, 80, 81	⊢
	: , : , :
76	instantiation	102, 82, 83	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
78	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
79	instantiation	102, 85, 84	,  ⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
81	instantiation	102, 85, 95	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
84	instantiation	102, 86, 87	,  ⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
86	instantiation	88, 89, 90	⊢
	: , :
87	assumption		⊢
88	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
89	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
90	instantiation	91, 92, 93	⊢
	: , :
91	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
92	instantiation	94, 95, 96	⊢
	: , :
93	instantiation	97, 98	⊢
	:
94	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
95	instantiation	102, 103, 99	⊢
	: , : , :
96	instantiation	102, 100, 101	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.negation.int_closure
98	instantiation	102, 103, 104	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
100	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
101	assumption		⊢
102	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
103	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat1