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, 3*, 4*, 5*	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	modus ponens	6, 7	⊢
3	instantiation	8, 80	⊢
	: , :
4	instantiation	8, 80	⊢
	: , :
5	instantiation	9, 10	⊢
	: , :
6	instantiation	11, 17	⊢
	: , : , : , : , : , : , :
7	generalization	12	⊢
8	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	modus ponens	13, 14	⊢
11	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
12	instantiation	15, 94, 80	,  ⊢
	: , :
13	instantiation	16, 97, 17, 56, 18, 57	⊢
	: , : , : , : , : , : , : , : , : , : , :
14	generalization	19	⊢
15	theorem		⊢
	proveit.physics.quantum.algebra.prepend_num_ket_with_zero_ket
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
17	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
18	instantiation	20, 27, 22, 23, 29	⊢
	: , : , :
19	instantiation	21, 27, 22, 23, 29, 24, 25, 26	,  ⊢
	: , : , : , :
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
22	instantiation	66	⊢
	: , :
23	instantiation	32, 27	⊢
	:
24	instantiation	66	⊢
	: , :
25	theorem		⊢
	proveit.physics.quantum.algebra.ket_zero_in_qubit_space
26	instantiation	28, 29, 30, 31	,  ⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
29	instantiation	32, 33	⊢
	:
30	instantiation	34, 35, 36	,  ⊢
	: , :
31	instantiation	37, 94, 80	,  ⊢
	: , :
32	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
33	instantiation	38, 92, 89	⊢
	: , :
34	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
35	instantiation	95, 70, 39	⊢
	: , : , :
36	instantiation	47, 40, 41	,  ⊢
	: , : , :
37	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
38	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
39	instantiation	95, 75, 42	⊢
	: , : , :
40	instantiation	63, 50, 43	,  ⊢
	: , :
41	instantiation	44, 45, 46	,  ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
43	instantiation	47, 48, 49	,  ⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.equals_transitivity
45	instantiation	55, 97, 51, 56, 53, 57, 50, 64, 65, 59	,  ⊢
	: , : , : , : , : , :
46	instantiation	55, 56, 92, 51, 57, 52, 53, 60, 61, 64, 65, 59	,  ⊢
	: , : , : , : , : , :
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
*equality replacement requirements