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