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	5	⊢
2	instantiation	64, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	modus ponens	7, 8	⊢
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	9, 10	⊢
	: , :
7	instantiation	11, 78, 115, 120, 12, 79, 13	⊢
	: , : , : , : , : , : , : , :
8	instantiation	14, 15, 16	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	instantiation	17, 33, 78, 120, 79, 32, 41, 34, 25	⊢
	: , : , : , : , : , : , : , : , : , :
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_factorization_from_add
12	instantiation	46, 18	⊢
	:
13	instantiation	89	⊢
	: , :
14	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
15	instantiation	19, 38, 20, 47	⊢
	: , : , :
16	instantiation	21, 38, 22, 32, 41, 23, 24, 25	⊢
	: , : , : , :
17	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
18	instantiation	26, 38, 47	⊢
	: , :
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
20	instantiation	89	⊢
	: , :
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
22	instantiation	89	⊢
	: , :
23	instantiation	89	⊢
	: , :
24	instantiation	27, 32, 28, 29	⊢
	: , : , : , :
25	modus ponens	30, 31	⊢
26	theorem		⊢
	proveit.numbers.multiplication.mult_nat_pos_closure_bin
27	theorem		⊢
	proveit.linear_algebra.addition.binary_closure
28	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
29	instantiation	40, 32, 33, 34	⊢
	: , : , : , :
30	instantiation	35, 36, 41	⊢
	: , : , : , : , : , :
31	generalization	37	⊢
32	instantiation	46, 38	⊢
	:
33	instantiation	48, 49, 39	⊢
	: , :
34	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
35	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
37	instantiation	40, 41, 42, 43	,  ⊢
	: , : , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	instantiation	68, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
41	instantiation	46, 47	⊢
	:
42	instantiation	48, 49, 50	,  ⊢
	: , :
43	instantiation	51, 117, 103	,  ⊢
	: , :
44	instantiation	86, 71, 52	⊢
	: , :
45	instantiation	64, 53, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
47	instantiation	55, 115, 112	⊢
	: , :
48	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
49	instantiation	118, 93, 56	⊢
	: , : , :
50	instantiation	68, 57, 58	,  ⊢
	: , : , :
51	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
52	instantiation	68, 59, 60	⊢
	: , : , :
53	instantiation	77, 120, 72, 78, 61, 79, 71, 87, 88, 67	⊢
	: , : , : , : , : , :
54	instantiation	77, 78, 115, 72, 79, 73, 61, 82, 83, 87, 88, 67	⊢
	: , : , : , : , : , :
55	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
56	instantiation	118, 98, 62	⊢
	: , : , :
57	instantiation	86, 71, 63	,  ⊢
	: , :
58	instantiation	64, 65, 66	,  ⊢
	: , : , :
59	instantiation	86, 76, 67	⊢
	: , :
60	instantiation	77, 78, 115, 120, 79, 80, 87, 88, 67	⊢
	: , : , : , : , : , :
61	instantiation	84	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
63	instantiation	68, 69, 70	,  ⊢
	: , : , :
64	axiom		⊢
	proveit.logic.equality.equals_transitivity
65	instantiation	77, 120, 72, 78, 74, 79, 71, 87, 88, 81	,  ⊢
	: , : , : , : , : , :
66	instantiation	77, 78, 115, 72, 79, 73, 74, 82, 83, 87, 88, 81	,  ⊢
	: , : , : , : , : , :
67	instantiation	118, 93, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.equality.sub_right_side_into
69	instantiation	86, 76, 81	,  ⊢
	: , :
70	instantiation	77, 78, 115, 120, 79, 80, 87, 88, 81	,  ⊢
	: , : , : , : , : , :
71	instantiation	86, 82, 83	⊢
	: , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
73	instantiation	89	⊢
	: , :
74	instantiation	84	⊢
	: , : , :
75	instantiation	118, 96, 85	⊢
	: , : , :
76	instantiation	86, 87, 88	⊢
	: , :
77	theorem		⊢
	proveit.numbers.multiplication.disassociation
78	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
79	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
80	instantiation	89	⊢
	: , :
81	instantiation	118, 93, 90	,  ⊢
	: , : , :
82	instantiation	118, 93, 91	⊢
	: , : , :
83	instantiation	118, 93, 92	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
85	instantiation	118, 101, 108	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
88	instantiation	118, 93, 94	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
90	instantiation	118, 96, 95	,  ⊢
	: , : , :
91	instantiation	118, 96, 97	⊢
	: , : , :
92	instantiation	118, 98, 99	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
94	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
95	instantiation	118, 101, 100	,  ⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
97	instantiation	118, 101, 111	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
100	instantiation	118, 102, 103	,  ⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
102	instantiation	104, 105, 106	⊢
	: , :
103	assumption		⊢
104	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
105	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
106	instantiation	107, 108, 109	⊢
	: , :
107	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
108	instantiation	110, 111, 112	⊢
	: , :
109	instantiation	113, 114	⊢
	:
110	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
111	instantiation	118, 119, 115	⊢
	: , : , :
112	instantiation	118, 116, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.negation.int_closure
114	instantiation	118, 119, 120	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
116	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
117	assumption		⊢
118	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
119	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat1