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