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