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