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