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	⊢
	: , : , : , :
1	reference	22	⊢
2	reference	23	⊢
3	instantiation	18, 5, 6, 7	⊢
	: , :
4	modus ponens	8, 9	⊢
5	instantiation	130, 101, 10	⊢
	: , : , :
6	instantiation	33, 80, 11	⊢
	: , :
7	instantiation	12, 13, 14	⊢
	: , : , :
8	instantiation	15, 109, 23	⊢
	: , : , : , : , : , :
9	generalization	16	⊢
10	instantiation	130, 104, 17	⊢
	: , : , :
11	instantiation	18, 49, 80, 29	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	19, 84, 20	⊢
	: , :
14	instantiation	46, 21	⊢
	: , : , :
15	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
16	instantiation	22, 23, 24, 25	,  ⊢
	: , : , : , :
17	instantiation	130, 113, 126	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.division.div_complex_closure
19	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
20	instantiation	130, 26, 27	⊢
	: , : , :
21	instantiation	28, 49, 80, 29, 30*	⊢
	: , :
22	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
23	instantiation	31, 32	⊢
	:
24	instantiation	33, 34, 35	,  ⊢
	: , :
25	instantiation	36, 129, 115	,  ⊢
	: , :
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
27	instantiation	37, 88, 38	⊢
	: , :
28	theorem		⊢
	proveit.numbers.division.div_as_mult
29	instantiation	39, 111	⊢
	:
30	instantiation	53, 40, 41	⊢
	: , : , :
31	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
32	instantiation	42, 127, 124	⊢
	: , :
33	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
34	instantiation	130, 101, 43	⊢
	: , : , :
35	instantiation	61, 44, 45	,  ⊢
	: , : , :
36	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
37	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
38	instantiation	130, 110, 129	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40	instantiation	46, 47	⊢
	: , : , :
41	instantiation	48, 49, 50	⊢
	: , :
42	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
43	instantiation	130, 106, 51	⊢
	: , : , :
44	instantiation	89, 64, 52	,  ⊢
	: , :
45	instantiation	53, 54, 55	,  ⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	56, 57, 109, 58*	⊢
	: , :
48	theorem		⊢
	proveit.numbers.multiplication.commutation
49	instantiation	130, 101, 59	⊢
	: , : , :
50	instantiation	130, 101, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
52	instantiation	61, 62, 63	,  ⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_transitivity
54	instantiation	75, 132, 65, 76, 67, 77, 64, 90, 91, 79	,  ⊢
	: , : , : , : , : , :
55	instantiation	75, 76, 127, 65, 77, 66, 67, 80, 81, 90, 91, 79	,  ⊢
	: , : , : , : , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
57	instantiation	130, 68, 69	⊢
	: , : , :
58	instantiation	70, 80	⊢
	:
59	instantiation	71, 72, 129	⊢
	: , : , :
60	instantiation	130, 104, 73	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.equality.sub_right_side_into
62	instantiation	89, 74, 79	,  ⊢
	: , :
63	instantiation	75, 76, 127, 132, 77, 78, 90, 91, 79	,  ⊢
	: , : , : , : , : , :
64	instantiation	89, 80, 81	⊢
	: , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
66	instantiation	92	⊢
	: , :
67	instantiation	82	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
69	instantiation	130, 83, 84	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
71	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
72	instantiation	85, 86	⊢
	: , :
73	instantiation	130, 87, 88	⊢
	: , : , :
74	instantiation	89, 90, 91	⊢
	: , :
75	theorem		⊢
	proveit.numbers.multiplication.disassociation
76	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
77	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
78	instantiation	92	⊢
	: , :
79	instantiation	130, 101, 93	,  ⊢
	: , : , :
80	instantiation	130, 101, 94	⊢
	: , : , :
81	instantiation	130, 101, 95	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
84	instantiation	130, 96, 97	⊢
	: , : , :
85	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
86	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
88	instantiation	98, 99, 100	⊢
	: , :
89	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
91	instantiation	130, 101, 102	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
93	instantiation	130, 104, 103	,  ⊢
	: , : , :
94	instantiation	130, 104, 105	⊢
	: , : , :
95	instantiation	130, 106, 107	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
97	instantiation	130, 108, 111	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
99	instantiation	130, 110, 109	⊢
	: , : , :
100	instantiation	130, 110, 111	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
102	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
103	instantiation	130, 113, 112	,  ⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
105	instantiation	130, 113, 123	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
110	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
112	instantiation	130, 114, 115	,  ⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
114	instantiation	116, 117, 118	⊢
	: , :
115	assumption		⊢
116	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
117	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
118	instantiation	119, 120, 121	⊢
	: , :
119	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
120	instantiation	122, 123, 124	⊢
	: , :
121	instantiation	125, 126	⊢
	:
122	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
123	instantiation	130, 131, 127	⊢
	: , : , :
124	instantiation	130, 128, 129	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.negation.int_closure
126	instantiation	130, 131, 132	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
128	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
129	assumption		⊢
130	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements