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