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