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	modus ponens	1, 2	⊢
1	instantiation	3, 4	⊢
	: , : , : , : , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	44, 6, 7	,  ⊢
	: , : , :
6	instantiation	8, 9, 10	,  ⊢
	: , : , :
7	instantiation	36, 11, 12	,  ⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	13, 14	,  ⊢
	: , : , :
10	instantiation	15, 16, 17, 18	,  ⊢
	: , : , :
11	instantiation	39, 19	,  ⊢
	: , :
12	instantiation	20, 95, 81	,  ⊢
	: , :
13	axiom		⊢
	proveit.logic.equality.substitution
14	instantiation	21, 22, 93, 55, 23, 24, 56, 59, 60, 64, 65, 52, 58	,  ⊢
	: , : , : , : , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
17	instantiation	44, 25, 26	,  ⊢
	: , : , :
18	instantiation	44, 27, 28	⊢
	: , : , :
19	instantiation	29, 30	,  ⊢
	: , : , :
20	theorem		⊢
	proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket
21	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
23	instantiation	31	⊢
	: , : , : , :
24	instantiation	66	⊢
	: , :
25	instantiation	63, 47, 32	,  ⊢
	: , :
26	instantiation	36, 33, 34	,  ⊢
	: , : , :
27	instantiation	63, 47, 35	⊢
	: , :
28	instantiation	36, 37, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_eq
30	instantiation	39, 40	,  ⊢
	: , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
32	instantiation	44, 41, 42	,  ⊢
	: , : , :
33	instantiation	54, 98, 48, 55, 43, 56, 47, 64, 65, 52	,  ⊢
	: , : , : , : , : , :
34	instantiation	54, 55, 93, 48, 56, 49, 43, 59, 60, 64, 65, 52	,  ⊢
	: , : , : , : , : , :
35	instantiation	44, 45, 46	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	54, 98, 48, 55, 50, 56, 47, 64, 65, 58	⊢
	: , : , : , : , : , :
38	instantiation	54, 55, 93, 48, 56, 49, 50, 59, 60, 64, 65, 58	⊢
	: , : , : , : , : , :
39	theorem		⊢
	proveit.logic.equality.equals_reversal
40	instantiation	51, 52, 58	,  ⊢
	: , :
41	instantiation	63, 53, 52	,  ⊢
	: , :
42	instantiation	54, 55, 93, 98, 56, 57, 64, 65, 52	,  ⊢
	: , : , : , : , : , :
43	instantiation	61	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.equality.sub_right_side_into
45	instantiation	63, 53, 58	⊢
	: , :
46	instantiation	54, 55, 93, 98, 56, 57, 64, 65, 58	⊢
	: , : , : , : , : , :
47	instantiation	63, 59, 60	⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
49	instantiation	66	⊢
	: , :
50	instantiation	61	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.commutation
52	instantiation	96, 71, 62	,  ⊢
	: , : , :
53	instantiation	63, 64, 65	⊢
	: , :
54	theorem		⊢
	proveit.numbers.multiplication.disassociation
55	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
56	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
57	instantiation	66	⊢
	: , :
58	instantiation	96, 71, 67	⊢
	: , : , :
59	instantiation	96, 71, 68	⊢
	: , : , :
60	instantiation	96, 71, 69	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
62	instantiation	96, 74, 70	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
65	instantiation	96, 71, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
67	instantiation	96, 74, 73	⊢
	: , : , :
68	instantiation	96, 74, 75	⊢
	: , : , :
69	instantiation	96, 76, 77	⊢
	: , : , :
70	instantiation	96, 79, 78	,  ⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
73	instantiation	96, 79, 86	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
75	instantiation	96, 79, 89	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
78	instantiation	96, 80, 81	,  ⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	instantiation	82, 83, 84	⊢
	: , :
81	assumption		⊢
82	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
83	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
84	instantiation	85, 86, 87	⊢
	: , :
85	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
86	instantiation	88, 89, 90	⊢
	: , :
87	instantiation	91, 92	⊢
	:
88	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
89	instantiation	96, 97, 93	⊢
	: , : , :
90	instantiation	96, 94, 95	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.negation.int_closure
92	instantiation	96, 97, 98	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
94	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
95	assumption		⊢
96	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
97	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat1