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