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, 6, 7, 8	⊢
	: , : , : , : , : , :
1	reference	106	⊢
2	reference	155	⊢
3	reference	150	⊢
4	reference	107	⊢
5	instantiation	121	⊢
	: , :
6	reference	108	⊢
7	instantiation	54, 9, 10, 11	⊢
	: , :
8	modus ponens	12, 13	⊢
9	instantiation	153, 125, 14	⊢
	: , : , :
10	instantiation	33, 111, 15	⊢
	: , :
11	instantiation	16, 17, 18	⊢
	: , : , :
12	instantiation	19	⊢
	: , : , :
13	generalization	20	⊢
14	instantiation	153, 131, 21	⊢
	: , : , :
15	instantiation	54, 48, 111, 30	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.sub_left_side_into
17	instantiation	22, 86, 23	⊢
	: , :
18	instantiation	45, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
20	instantiation	118, 25, 26	,  ⊢
	: , :
21	instantiation	153, 134, 149	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
23	instantiation	153, 27, 28	⊢
	: , : , :
24	instantiation	29, 48, 111, 30, 31*	⊢
	: , :
25	instantiation	33, 34, 32	⊢
	: , :
26	instantiation	33, 34, 35	,  ⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
28	instantiation	36, 90, 37	⊢
	: , :
29	theorem		⊢
	proveit.numbers.division.div_as_mult
30	instantiation	69, 117	⊢
	:
31	instantiation	80, 38, 39	⊢
	: , : , :
32	instantiation	92, 40, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
34	instantiation	153, 125, 42	⊢
	: , : , :
35	instantiation	43, 44	,  ⊢
	:
36	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
37	instantiation	153, 116, 152	⊢
	: , : , :
38	instantiation	45, 46	⊢
	: , : , :
39	instantiation	47, 48, 49	⊢
	: , :
40	instantiation	118, 95, 50	⊢
	: , :
41	instantiation	80, 51, 52	⊢
	: , : , :
42	instantiation	153, 129, 53	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.negation.complex_closure
44	instantiation	54, 55, 56, 57	,  ⊢
	: , :
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	58, 59, 115, 60*	⊢
	: , :
47	theorem		⊢
	proveit.numbers.multiplication.commutation
48	instantiation	153, 125, 61	⊢
	: , : , :
49	instantiation	153, 125, 62	⊢
	: , : , :
50	instantiation	92, 63, 64	⊢
	: , : , :
51	instantiation	106, 155, 96, 107, 65, 108, 95, 119, 91, 120	⊢
	: , : , : , : , : , :
52	instantiation	106, 107, 150, 96, 108, 97, 65, 111, 112, 119, 91, 120	⊢
	: , : , : , : , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
54	theorem		⊢
	proveit.numbers.division.div_complex_closure
55	instantiation	92, 66, 67	,  ⊢
	: , : , :
56	instantiation	153, 125, 68	⊢
	: , : , :
57	instantiation	69, 70	⊢
	:
58	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
59	instantiation	153, 71, 72	⊢
	: , : , :
60	instantiation	73, 111	⊢
	:
61	instantiation	74, 75, 152	⊢
	: , : , :
62	instantiation	153, 131, 76	⊢
	: , : , :
63	instantiation	118, 77, 120	⊢
	: , :
64	instantiation	106, 107, 150, 155, 108, 78, 119, 91, 120	⊢
	: , : , : , : , : , :
65	instantiation	113	⊢
	: , : , :
66	instantiation	118, 95, 79	,  ⊢
	: , :
67	instantiation	80, 81, 82	,  ⊢
	: , : , :
68	instantiation	153, 131, 83	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
70	instantiation	84, 150, 147	⊢
	: , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
72	instantiation	153, 85, 86	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
74	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
75	instantiation	87, 88	⊢
	: , :
76	instantiation	153, 89, 90	⊢
	: , : , :
77	instantiation	118, 119, 91	⊢
	: , :
78	instantiation	121	⊢
	: , :
79	instantiation	92, 93, 94	,  ⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.equals_transitivity
81	instantiation	106, 155, 96, 107, 98, 108, 95, 119, 120, 110	,  ⊢
	: , : , : , : , : , :
82	instantiation	106, 107, 150, 96, 108, 97, 98, 111, 112, 119, 120, 110	,  ⊢
	: , : , : , : , : , :
83	instantiation	153, 134, 143	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
86	instantiation	153, 99, 100	⊢
	: , : , :
87	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
90	instantiation	101, 102, 103	⊢
	: , :
91	instantiation	153, 125, 104	⊢
	: , : , :
92	theorem		⊢
	proveit.logic.equality.sub_right_side_into
93	instantiation	118, 105, 110	,  ⊢
	: , :
94	instantiation	106, 107, 150, 155, 108, 109, 119, 120, 110	,  ⊢
	: , : , : , : , : , :
95	instantiation	118, 111, 112	⊢
	: , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
97	instantiation	121	⊢
	: , :
98	instantiation	113	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
100	instantiation	153, 114, 117	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
102	instantiation	153, 116, 115	⊢
	: , : , :
103	instantiation	153, 116, 117	⊢
	: , : , :
104	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
105	instantiation	118, 119, 120	⊢
	: , :
106	theorem		⊢
	proveit.numbers.multiplication.disassociation
107	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
108	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
109	instantiation	121	⊢
	: , :
110	instantiation	153, 125, 122	⊢
	: , : , :
111	instantiation	153, 125, 123	⊢
	: , : , :
112	instantiation	153, 125, 124	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
114	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
115	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
118	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
119	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
120	instantiation	153, 125, 126	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
122	instantiation	153, 131, 127	⊢
	: , : , :
123	instantiation	153, 131, 128	⊢
	: , : , :
124	instantiation	153, 129, 130	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
126	instantiation	153, 131, 132	⊢
	: , : , :
127	instantiation	153, 134, 133	⊢
	: , : , :
128	instantiation	153, 134, 146	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	153, 134, 135	⊢
	: , : , :
133	instantiation	153, 137, 136	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
135	instantiation	153, 137, 138	⊢
	: , : , :
136	assumption		⊢
137	instantiation	139, 140, 141	⊢
	: , :
138	assumption		⊢
139	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
140	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
141	instantiation	142, 143, 144	⊢
	: , :
142	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
143	instantiation	145, 146, 147	⊢
	: , :
144	instantiation	148, 149	⊢
	:
145	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
146	instantiation	153, 154, 150	⊢
	: , : , :
147	instantiation	153, 151, 152	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.negation.int_closure
149	instantiation	153, 154, 155	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
151	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
152	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
153	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements