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, 3, 4, 5, 6, 7, 8, 9*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.association
2	reference	95	⊢
3	reference	155	⊢
4	reference	160	⊢
5	reference	96	⊢
6	instantiation	111	⊢
	: , :
7	reference	17	⊢
8	modus ponens	10, 11	⊢
9	instantiation	12, 17, 136, 13*, 14*	⊢
	: , : , :
10	instantiation	15	⊢
	: , : , :
11	generalization	16	⊢
12	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
13	instantiation	103, 17	⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
15	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
16	instantiation	108, 18, 19	,  ⊢
	: , :
17	instantiation	45, 20, 21, 22	⊢
	: , :
18	instantiation	27, 24, 23	⊢
	: , :
19	instantiation	27, 24, 25	,  ⊢
	: , :
20	instantiation	158, 121, 26	⊢
	: , : , :
21	instantiation	27, 104, 28	⊢
	: , :
22	instantiation	29, 30, 31	⊢
	: , : , :
23	instantiation	80, 32, 33	⊢
	: , : , :
24	instantiation	158, 121, 34	⊢
	: , : , :
25	instantiation	35, 36	,  ⊢
	:
26	instantiation	158, 132, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
28	instantiation	45, 77, 104, 52	⊢
	: , :
29	theorem		⊢
	proveit.logic.equality.sub_left_side_into
30	instantiation	38, 115, 39	⊢
	: , :
31	instantiation	74, 40	⊢
	: , : , :
32	instantiation	108, 83, 41	⊢
	: , :
33	instantiation	69, 42, 43	⊢
	: , : , :
34	instantiation	158, 124, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.negation.complex_closure
36	instantiation	45, 46, 47, 48	,  ⊢
	: , :
37	instantiation	158, 139, 154	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
39	instantiation	158, 49, 50	⊢
	: , : , :
40	instantiation	51, 77, 104, 52, 53*	⊢
	: , :
41	instantiation	80, 54, 55	⊢
	: , : , :
42	instantiation	94, 160, 84, 95, 56, 96, 83, 109, 79, 110	⊢
	: , : , : , : , : , :
43	instantiation	94, 95, 155, 84, 96, 85, 56, 104, 99, 109, 79, 110	⊢
	: , : , : , : , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
45	theorem		⊢
	proveit.numbers.division.div_complex_closure
46	instantiation	80, 57, 58	,  ⊢
	: , : , :
47	instantiation	158, 121, 59	⊢
	: , : , :
48	instantiation	63, 60	⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
50	instantiation	61, 120, 62	⊢
	: , :
51	theorem		⊢
	proveit.numbers.division.div_as_mult
52	instantiation	63, 138	⊢
	:
53	instantiation	69, 64, 65	⊢
	: , : , :
54	instantiation	108, 66, 110	⊢
	: , :
55	instantiation	94, 95, 155, 160, 96, 67, 109, 79, 110	⊢
	: , : , : , : , : , :
56	instantiation	100	⊢
	: , : , :
57	instantiation	108, 83, 68	,  ⊢
	: , :
58	instantiation	69, 70, 71	,  ⊢
	: , : , :
59	instantiation	158, 132, 72	⊢
	: , : , :
60	instantiation	73, 155, 152	⊢
	: , :
61	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
62	instantiation	158, 137, 157	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
64	instantiation	74, 75	⊢
	: , : , :
65	instantiation	76, 77, 78	⊢
	: , :
66	instantiation	108, 109, 79	⊢
	: , :
67	instantiation	111	⊢
	: , :
68	instantiation	80, 81, 82	,  ⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.equals_transitivity
70	instantiation	94, 160, 84, 95, 86, 96, 83, 109, 110, 98	,  ⊢
	: , : , : , : , : , :
71	instantiation	94, 95, 155, 84, 96, 85, 86, 104, 99, 109, 110, 98	,  ⊢
	: , : , : , : , : , :
72	instantiation	158, 139, 148	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
74	axiom		⊢
	proveit.logic.equality.substitution
75	instantiation	87, 88, 136, 89*	⊢
	: , :
76	theorem		⊢
	proveit.numbers.multiplication.commutation
77	instantiation	158, 121, 90	⊢
	: , : , :
78	instantiation	158, 121, 91	⊢
	: , : , :
79	instantiation	158, 121, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.logic.equality.sub_right_side_into
81	instantiation	108, 93, 98	,  ⊢
	: , :
82	instantiation	94, 95, 155, 160, 96, 97, 109, 110, 98	,  ⊢
	: , : , : , : , : , :
83	instantiation	108, 104, 99	⊢
	: , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
85	instantiation	111	⊢
	: , :
86	instantiation	100	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
88	instantiation	158, 101, 102	⊢
	: , : , :
89	instantiation	103, 104	⊢
	:
90	instantiation	105, 106, 157	⊢
	: , : , :
91	instantiation	158, 132, 107	⊢
	: , : , :
92	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
93	instantiation	108, 109, 110	⊢
	: , :
94	theorem		⊢
	proveit.numbers.multiplication.disassociation
95	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
96	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
97	instantiation	111	⊢
	: , :
98	instantiation	158, 121, 112	⊢
	: , : , :
99	instantiation	158, 121, 113	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
101	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
102	instantiation	158, 114, 115	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
104	instantiation	158, 121, 116	⊢
	: , : , :
105	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
106	instantiation	117, 118	⊢
	: , :
107	instantiation	158, 119, 120	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
109	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
110	instantiation	158, 121, 122	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
112	instantiation	158, 132, 123	⊢
	: , : , :
113	instantiation	158, 124, 125	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
115	instantiation	158, 126, 127	⊢
	: , : , :
116	instantiation	158, 132, 128	⊢
	: , : , :
117	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
119	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
120	instantiation	129, 130, 131	⊢
	: , :
121	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
122	instantiation	158, 132, 133	⊢
	: , : , :
123	instantiation	158, 139, 134	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
125	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
126	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
127	instantiation	158, 135, 138	⊢
	: , : , :
128	instantiation	158, 139, 151	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
130	instantiation	158, 137, 136	⊢
	: , : , :
131	instantiation	158, 137, 138	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
133	instantiation	158, 139, 140	⊢
	: , : , :
134	instantiation	158, 142, 141	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
136	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
137	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
138	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
140	instantiation	158, 142, 143	⊢
	: , : , :
141	assumption		⊢
142	instantiation	144, 145, 146	⊢
	: , :
143	assumption		⊢
144	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
145	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
146	instantiation	147, 148, 149	⊢
	: , :
147	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
148	instantiation	150, 151, 152	⊢
	: , :
149	instantiation	153, 154	⊢
	:
150	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
151	instantiation	158, 159, 155	⊢
	: , : , :
152	instantiation	158, 156, 157	⊢
	: , : , :
153	theorem		⊢
	proveit.numbers.negation.int_closure
154	instantiation	158, 159, 160	⊢
	: , : , :
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
156	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
157	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
158	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
159	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
160	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements