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