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