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