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