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	modus ponens	1, 2	⊢
1	instantiation	3, 69, 106, 111, 4, 70, 5	⊢
	: , : , : , : , : , : , : , :
2	instantiation	6, 7, 8	⊢
	: , : , :
3	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_factorization_from_add
4	instantiation	37, 9	⊢
	:
5	instantiation	80	⊢
	: , :
6	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
7	instantiation	10, 29, 11, 38	⊢
	: , : , :
8	instantiation	12, 29, 13, 23, 32, 14, 15, 16	⊢
	: , : , : , :
9	instantiation	17, 29, 38	⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
11	instantiation	80	⊢
	: , :
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
13	instantiation	80	⊢
	: , :
14	instantiation	80	⊢
	: , :
15	instantiation	18, 23, 19, 20	⊢
	: , : , : , :
16	modus ponens	21, 22	⊢
17	theorem		⊢
	proveit.numbers.multiplication.mult_nat_pos_closure_bin
18	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
19	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
20	instantiation	31, 23, 24, 25	⊢
	: , : , : , :
21	instantiation	26, 27, 32	⊢
	: , : , : , : , : , :
22	generalization	28	⊢
23	instantiation	37, 29	⊢
	:
24	instantiation	39, 40, 30	⊢
	: , :
25	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
26	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
28	instantiation	31, 32, 33, 34	,  ⊢
	: , : , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
30	instantiation	59, 35, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
32	instantiation	37, 38	⊢
	:
33	instantiation	39, 40, 41	,  ⊢
	: , :
34	instantiation	42, 108, 94	,  ⊢
	: , :
35	instantiation	77, 62, 43	⊢
	: , :
36	instantiation	55, 44, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
38	instantiation	46, 106, 103	⊢
	: , :
39	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
40	instantiation	109, 84, 47	⊢
	: , : , :
41	instantiation	59, 48, 49	,  ⊢
	: , : , :
42	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
43	instantiation	59, 50, 51	⊢
	: , : , :
44	instantiation	68, 111, 63, 69, 52, 70, 62, 78, 79, 58	⊢
	: , : , : , : , : , :
45	instantiation	68, 69, 106, 63, 70, 64, 52, 73, 74, 78, 79, 58	⊢
	: , : , : , : , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
47	instantiation	109, 89, 53	⊢
	: , : , :
48	instantiation	77, 62, 54	,  ⊢
	: , :
49	instantiation	55, 56, 57	,  ⊢
	: , : , :
50	instantiation	77, 67, 58	⊢
	: , :
51	instantiation	68, 69, 106, 111, 70, 71, 78, 79, 58	⊢
	: , : , : , : , : , :
52	instantiation	75	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
54	instantiation	59, 60, 61	,  ⊢
	: , : , :
55	axiom		⊢
	proveit.logic.equality.equals_transitivity
56	instantiation	68, 111, 63, 69, 65, 70, 62, 78, 79, 72	,  ⊢
	: , : , : , : , : , :
57	instantiation	68, 69, 106, 63, 70, 64, 65, 73, 74, 78, 79, 72	,  ⊢
	: , : , : , : , : , :
58	instantiation	109, 84, 66	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.equality.sub_right_side_into
60	instantiation	77, 67, 72	,  ⊢
	: , :
61	instantiation	68, 69, 106, 111, 70, 71, 78, 79, 72	,  ⊢
	: , : , : , : , : , :
62	instantiation	77, 73, 74	⊢
	: , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
64	instantiation	80	⊢
	: , :
65	instantiation	75	⊢
	: , : , :
66	instantiation	109, 87, 76	⊢
	: , : , :
67	instantiation	77, 78, 79	⊢
	: , :
68	theorem		⊢
	proveit.numbers.multiplication.disassociation
69	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	80	⊢
	: , :
72	instantiation	109, 84, 81	,  ⊢
	: , : , :
73	instantiation	109, 84, 82	⊢
	: , : , :
74	instantiation	109, 84, 83	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
76	instantiation	109, 92, 99	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
79	instantiation	109, 84, 85	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
81	instantiation	109, 87, 86	,  ⊢
	: , : , :
82	instantiation	109, 87, 88	⊢
	: , : , :
83	instantiation	109, 89, 90	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
85	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
86	instantiation	109, 92, 91	,  ⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
88	instantiation	109, 92, 102	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
91	instantiation	109, 93, 94	,  ⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
93	instantiation	95, 96, 97	⊢
	: , :
94	assumption		⊢
95	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
96	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
97	instantiation	98, 99, 100	⊢
	: , :
98	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
99	instantiation	101, 102, 103	⊢
	: , :
100	instantiation	104, 105	⊢
	:
101	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
102	instantiation	109, 110, 106	⊢
	: , : , :
103	instantiation	109, 107, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.negation.int_closure
105	instantiation	109, 110, 111	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
107	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
108	assumption		⊢
109	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
111	theorem		⊢
	proveit.numbers.numerals.decimals.nat1