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