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	modus ponens	1, 2	⊢
1	instantiation	3, 129	⊢
	: , : , : , : , : , : , :
2	generalization	4	⊢
3	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
4	instantiation	62, 5, 6	,  ⊢
	: , : , :
5	instantiation	7, 88, 153, 89, 11, 10, 12	,  ⊢
	: , : , : , : , : , : , :
6	instantiation	8, 153, 148, 88, 9, 89, 10, 11, 12	,  ⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
8	theorem		⊢
	proveit.numbers.multiplication.association
9	instantiation	104	⊢
	: , :
10	instantiation	38, 13, 14, 15	⊢
	: , :
11	instantiation	20, 17, 16	⊢
	: , :
12	instantiation	20, 17, 18	,  ⊢
	: , :
13	instantiation	151, 114, 19	⊢
	: , : , :
14	instantiation	20, 97, 21	⊢
	: , :
15	instantiation	22, 23, 24	⊢
	: , : , :
16	instantiation	73, 25, 26	⊢
	: , : , :
17	instantiation	151, 114, 27	⊢
	: , : , :
18	instantiation	28, 29	,  ⊢
	:
19	instantiation	151, 125, 30	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
21	instantiation	38, 70, 97, 45	⊢
	: , :
22	theorem		⊢
	proveit.logic.equality.sub_left_side_into
23	instantiation	31, 108, 32	⊢
	: , :
24	instantiation	67, 33	⊢
	: , : , :
25	instantiation	101, 76, 34	⊢
	: , :
26	instantiation	62, 35, 36	⊢
	: , : , :
27	instantiation	151, 117, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.negation.complex_closure
29	instantiation	38, 39, 40, 41	,  ⊢
	: , :
30	instantiation	151, 132, 147	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
32	instantiation	151, 42, 43	⊢
	: , : , :
33	instantiation	44, 70, 97, 45, 46*	⊢
	: , :
34	instantiation	73, 47, 48	⊢
	: , : , :
35	instantiation	87, 153, 77, 88, 49, 89, 76, 102, 72, 103	⊢
	: , : , : , : , : , :
36	instantiation	87, 88, 148, 77, 89, 78, 49, 97, 92, 102, 72, 103	⊢
	: , : , : , : , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
38	theorem		⊢
	proveit.numbers.division.div_complex_closure
39	instantiation	73, 50, 51	,  ⊢
	: , : , :
40	instantiation	151, 114, 52	⊢
	: , : , :
41	instantiation	56, 53	⊢
	:
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
43	instantiation	54, 113, 55	⊢
	: , :
44	theorem		⊢
	proveit.numbers.division.div_as_mult
45	instantiation	56, 131	⊢
	:
46	instantiation	62, 57, 58	⊢
	: , : , :
47	instantiation	101, 59, 103	⊢
	: , :
48	instantiation	87, 88, 148, 153, 89, 60, 102, 72, 103	⊢
	: , : , : , : , : , :
49	instantiation	93	⊢
	: , : , :
50	instantiation	101, 76, 61	,  ⊢
	: , :
51	instantiation	62, 63, 64	,  ⊢
	: , : , :
52	instantiation	151, 125, 65	⊢
	: , : , :
53	instantiation	66, 148, 145	⊢
	: , :
54	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
55	instantiation	151, 130, 150	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
57	instantiation	67, 68	⊢
	: , : , :
58	instantiation	69, 70, 71	⊢
	: , :
59	instantiation	101, 102, 72	⊢
	: , :
60	instantiation	104	⊢
	: , :
61	instantiation	73, 74, 75	,  ⊢
	: , : , :
62	axiom		⊢
	proveit.logic.equality.equals_transitivity
63	instantiation	87, 153, 77, 88, 79, 89, 76, 102, 103, 91	,  ⊢
	: , : , : , : , : , :
64	instantiation	87, 88, 148, 77, 89, 78, 79, 97, 92, 102, 103, 91	,  ⊢
	: , : , : , : , : , :
65	instantiation	151, 132, 141	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
67	axiom		⊢
	proveit.logic.equality.substitution
68	instantiation	80, 81, 129, 82*	⊢
	: , :
69	theorem		⊢
	proveit.numbers.multiplication.commutation
70	instantiation	151, 114, 83	⊢
	: , : , :
71	instantiation	151, 114, 84	⊢
	: , : , :
72	instantiation	151, 114, 85	⊢
	: , : , :
73	theorem		⊢
	proveit.logic.equality.sub_right_side_into
74	instantiation	101, 86, 91	,  ⊢
	: , :
75	instantiation	87, 88, 148, 153, 89, 90, 102, 103, 91	,  ⊢
	: , : , : , : , : , :
76	instantiation	101, 97, 92	⊢
	: , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
78	instantiation	104	⊢
	: , :
79	instantiation	93	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
81	instantiation	151, 94, 95	⊢
	: , : , :
82	instantiation	96, 97	⊢
	:
83	instantiation	98, 99, 150	⊢
	: , : , :
84	instantiation	151, 125, 100	⊢
	: , : , :
85	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
86	instantiation	101, 102, 103	⊢
	: , :
87	theorem		⊢
	proveit.numbers.multiplication.disassociation
88	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
89	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
90	instantiation	104	⊢
	: , :
91	instantiation	151, 114, 105	⊢
	: , : , :
92	instantiation	151, 114, 106	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
94	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
95	instantiation	151, 107, 108	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
97	instantiation	151, 114, 109	⊢
	: , : , :
98	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
99	instantiation	110, 111	⊢
	: , :
100	instantiation	151, 112, 113	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
103	instantiation	151, 114, 115	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
105	instantiation	151, 125, 116	⊢
	: , : , :
106	instantiation	151, 117, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
108	instantiation	151, 119, 120	⊢
	: , : , :
109	instantiation	151, 125, 121	⊢
	: , : , :
110	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
111	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
113	instantiation	122, 123, 124	⊢
	: , :
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
115	instantiation	151, 125, 126	⊢
	: , : , :
116	instantiation	151, 132, 127	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
120	instantiation	151, 128, 131	⊢
	: , : , :
121	instantiation	151, 132, 144	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
123	instantiation	151, 130, 129	⊢
	: , : , :
124	instantiation	151, 130, 131	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
126	instantiation	151, 132, 133	⊢
	: , : , :
127	instantiation	151, 135, 134	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
131	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
132	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
133	instantiation	151, 135, 136	⊢
	: , : , :
134	assumption		⊢
135	instantiation	137, 138, 139	⊢
	: , :
136	assumption		⊢
137	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
138	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
139	instantiation	140, 141, 142	⊢
	: , :
140	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
141	instantiation	143, 144, 145	⊢
	: , :
142	instantiation	146, 147	⊢
	:
143	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
144	instantiation	151, 152, 148	⊢
	: , : , :
145	instantiation	151, 149, 150	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.negation.int_closure
147	instantiation	151, 152, 153	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
149	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
150	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
151	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
152	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
153	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements