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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4	⊢
	: , :
3	theorem		⊢
	proveit.logic.equality.equals_reversal
4	instantiation	5, 6, 56, 97, 57, 7, 23, 8, 9	⊢
	: , : , : , : , : , : , : , : , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
6	instantiation	31, 32, 10	⊢
	: , :
7	instantiation	29, 11	⊢
	:
8	theorem		⊢
	proveit.physics.quantum.algebra.ket_one_in_qubit_space
9	modus ponens	12, 13	⊢
10	instantiation	47, 14, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
12	instantiation	16, 17, 23	⊢
	: , : , : , : , : , :
13	generalization	18	⊢
14	instantiation	63, 50, 19	⊢
	: , :
15	instantiation	43, 20, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
18	instantiation	22, 23, 24, 25	,  ⊢
	: , : , : , :
19	instantiation	47, 26, 27	⊢
	: , : , :
20	instantiation	55, 97, 51, 56, 28, 57, 50, 64, 65, 35	⊢
	: , : , : , : , : , :
21	instantiation	55, 56, 92, 51, 57, 52, 28, 60, 61, 64, 65, 35	⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
23	instantiation	29, 30	⊢
	:
24	instantiation	31, 32, 33	,  ⊢
	: , :
25	instantiation	34, 94, 80	,  ⊢
	: , :
26	instantiation	63, 54, 35	⊢
	: , :
27	instantiation	55, 56, 92, 97, 57, 58, 64, 65, 35	⊢
	: , : , : , : , : , :
28	instantiation	62	⊢
	: , : , :
29	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
30	instantiation	36, 92, 89	⊢
	: , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
32	instantiation	95, 70, 37	⊢
	: , : , :
33	instantiation	47, 38, 39	,  ⊢
	: , : , :
34	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
35	instantiation	95, 70, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
37	instantiation	95, 75, 41	⊢
	: , : , :
38	instantiation	63, 50, 42	,  ⊢
	: , :
39	instantiation	43, 44, 45	,  ⊢
	: , : , :
40	instantiation	95, 73, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
42	instantiation	47, 48, 49	,  ⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	55, 97, 51, 56, 53, 57, 50, 64, 65, 59	,  ⊢
	: , : , : , : , : , :
45	instantiation	55, 56, 92, 51, 57, 52, 53, 60, 61, 64, 65, 59	,  ⊢
	: , : , : , : , : , :
46	instantiation	95, 78, 85	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.sub_right_side_into
48	instantiation	63, 54, 59	,  ⊢
	: , :
49	instantiation	55, 56, 92, 97, 57, 58, 64, 65, 59	,  ⊢
	: , : , : , : , : , :
50	instantiation	63, 60, 61	⊢
	: , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
52	instantiation	66	⊢
	: , :
53	instantiation	62	⊢
	: , : , :
54	instantiation	63, 64, 65	⊢
	: , :
55	theorem		⊢
	proveit.numbers.multiplication.disassociation
56	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
57	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
58	instantiation	66	⊢
	: , :
59	instantiation	95, 70, 67	,  ⊢
	: , : , :
60	instantiation	95, 70, 68	⊢
	: , : , :
61	instantiation	95, 70, 69	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
63	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
65	instantiation	95, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
67	instantiation	95, 73, 72	,  ⊢
	: , : , :
68	instantiation	95, 73, 74	⊢
	: , : , :
69	instantiation	95, 75, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
71	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
72	instantiation	95, 78, 77	,  ⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
74	instantiation	95, 78, 88	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
77	instantiation	95, 79, 80	,  ⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
79	instantiation	81, 82, 83	⊢
	: , :
80	assumption		⊢
81	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
82	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
83	instantiation	84, 85, 86	⊢
	: , :
84	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
85	instantiation	87, 88, 89	⊢
	: , :
86	instantiation	90, 91	⊢
	:
87	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
88	instantiation	95, 96, 92	⊢
	: , : , :
89	instantiation	95, 93, 94	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.negation.int_closure
91	instantiation	95, 96, 97	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
93	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
94	assumption		⊢
95	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
96	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
97	theorem		⊢
	proveit.numbers.numerals.decimals.nat1