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