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	reference	108	⊢
2	instantiation	80, 4	⊢
	: , : , :
3	instantiation	5, 160, 161, 32, 6*	⊢
	: , : , :
4	modus ponens	7, 8	⊢
5	theorem		⊢
	proveit.numbers.summation.trivial_sum
6	instantiation	108, 9, 86	⊢
	: , : , :
7	instantiation	10, 127	⊢
	: , : , : , : , : , :
8	generalization	11	⊢
9	instantiation	80, 12	⊢
	: , : , :
10	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
11	instantiation	13, 14	⊢
	: , : , :
12	instantiation	108, 15, 16	⊢
	: , : , :
13	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
14	deduction	17	⊢
15	instantiation	80, 18	⊢
	: , : , :
16	instantiation	19, 20, 21, 22	⊢
	: , : , : , :
17	instantiation	108, 23, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.negation.negated_zero
19	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
20	instantiation	25, 130, 156, 131, 29, 26, 103, 30, 27, 32	⊢
	: , : , : , : , : , :
21	instantiation	28, 156, 171, 29, 103, 30, 32	⊢
	: , : , : , :
22	instantiation	31, 32, 103, 33	⊢
	: , : , :
23	instantiation	80, 34	⊢
	: , : , :
24	instantiation	35, 66, 36, 58, 37*	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.addition.disassociation
26	instantiation	142	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
28	theorem		⊢
	proveit.numbers.addition.elim_zero_any
29	instantiation	142	⊢
	: , :
30	instantiation	169, 146, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
32	instantiation	169, 146, 39	⊢
	: , : , :
33	instantiation	52	⊢
	:
34	instantiation	40, 41, 42, 43, 44, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
36	instantiation	46, 85	⊢
	:
37	instantiation	108, 47, 48	⊢
	: , : , :
38	instantiation	169, 151, 49	⊢
	: , : , :
39	instantiation	169, 151, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	instantiation	142	⊢
	: , :
43	instantiation	142	⊢
	: , :
44	instantiation	80, 51	⊢
	: , : , :
45	instantiation	52	⊢
	:
46	theorem		⊢
	proveit.numbers.negation.complex_closure
47	instantiation	80, 53	⊢
	: , : , :
48	instantiation	54, 55	⊢
	:
49	instantiation	169, 154, 164	⊢
	: , : , :
50	instantiation	169, 154, 168	⊢
	: , : , :
51	instantiation	80, 56	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.equals_reflexivity
53	instantiation	57, 85, 58, 59	⊢
	: , :
54	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
55	instantiation	169, 146, 60	⊢
	: , : , :
56	instantiation	108, 61, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
58	instantiation	117, 63, 64	⊢
	: , : , :
59	instantiation	97, 121, 171, 130, 65, 131, 134, 135, 140, 141, 133	⊢
	: , : , : , : , : , : , :
60	instantiation	169, 149, 66	⊢
	: , : , :
61	instantiation	80, 67	⊢
	: , : , :
62	instantiation	108, 68, 69	⊢
	: , : , :
63	instantiation	139, 120, 70	⊢
	: , :
64	instantiation	108, 71, 72	⊢
	: , : , :
65	instantiation	136	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
67	instantiation	129, 98, 156, 130, 99, 73, 131, 134, 135, 140, 141, 103, 133	⊢
	: , : , : , : , : , :
68	instantiation	108, 74, 75	⊢
	: , : , :
69	instantiation	76, 85	⊢
	:
70	instantiation	117, 77, 78	⊢
	: , : , :
71	instantiation	129, 171, 121, 130, 79, 131, 120, 140, 133, 141	⊢
	: , : , : , : , : , :
72	instantiation	129, 130, 156, 121, 131, 122, 79, 134, 135, 140, 133, 141	⊢
	: , : , : , : , : , :
73	instantiation	142	⊢
	: , :
74	instantiation	80, 81	⊢
	: , : , :
75	instantiation	82, 83, 84, 85, 86*	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.division.frac_one_denom
77	instantiation	139, 87, 141	⊢
	: , :
78	instantiation	129, 130, 156, 171, 131, 88, 140, 133, 141	⊢
	: , : , : , : , : , :
79	instantiation	136	⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.substitution
81	instantiation	108, 89, 90	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.division.frac_cancel_left
83	instantiation	169, 92, 91	⊢
	: , : , :
84	instantiation	169, 92, 93	⊢
	: , : , :
85	instantiation	117, 94, 95	⊢
	: , : , :
86	instantiation	96, 103	⊢
	:
87	instantiation	139, 140, 133	⊢
	: , :
88	instantiation	142	⊢
	: , :
89	instantiation	97, 130, 98, 171, 131, 99, 134, 135, 140, 141, 103, 133	⊢
	: , : , : , : , : , : , :
90	instantiation	100, 171, 101, 130, 102, 131, 103, 134, 135, 140, 141, 133	⊢
	: , : , : , : , : , :
91	instantiation	169, 105, 104	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
93	instantiation	169, 105, 106	⊢
	: , : , :
94	instantiation	139, 120, 107	⊢
	: , :
95	instantiation	108, 109, 110	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
97	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
99	instantiation	111	⊢
	: , : , : , :
100	theorem		⊢
	proveit.numbers.multiplication.association
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
102	instantiation	112	⊢
	: , : , : , : , :
103	instantiation	169, 146, 113	⊢
	: , : , :
104	instantiation	169, 115, 114	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
106	instantiation	169, 115, 116	⊢
	: , : , :
107	instantiation	117, 118, 119	⊢
	: , : , :
108	axiom		⊢
	proveit.logic.equality.equals_transitivity
109	instantiation	129, 171, 121, 130, 123, 131, 120, 140, 141, 133	⊢
	: , : , : , : , : , :
110	instantiation	129, 130, 156, 121, 131, 122, 123, 134, 135, 140, 141, 133	⊢
	: , : , : , : , : , :
111	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
112	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
113	instantiation	124, 125, 166	⊢
	: , : , :
114	instantiation	169, 126, 166	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
116	instantiation	169, 126, 127	⊢
	: , : , :
117	theorem		⊢
	proveit.logic.equality.sub_right_side_into
118	instantiation	139, 128, 133	⊢
	: , :
119	instantiation	129, 130, 156, 171, 131, 132, 140, 141, 133	⊢
	: , : , : , : , : , :
120	instantiation	139, 134, 135	⊢
	: , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
122	instantiation	142	⊢
	: , :
123	instantiation	136	⊢
	: , : , :
124	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
125	instantiation	137, 138	⊢
	: , :
126	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
128	instantiation	139, 140, 141	⊢
	: , :
129	theorem		⊢
	proveit.numbers.multiplication.disassociation
130	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
131	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
132	instantiation	142	⊢
	: , :
133	instantiation	169, 146, 143	⊢
	: , : , :
134	instantiation	169, 146, 144	⊢
	: , : , :
135	instantiation	169, 146, 145	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
137	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
139	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
140	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
141	instantiation	169, 146, 147	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
143	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
144	instantiation	169, 151, 148	⊢
	: , : , :
145	instantiation	169, 149, 150	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
147	instantiation	169, 151, 152	⊢
	: , : , :
148	instantiation	169, 154, 153	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
150	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
151	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
152	instantiation	169, 154, 155	⊢
	: , : , :
153	instantiation	169, 170, 156	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
155	instantiation	169, 157, 158	⊢
	: , : , :
156	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
157	instantiation	159, 160, 161	⊢
	: , :
158	assumption		⊢
159	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
160	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
161	instantiation	162, 163, 164	⊢
	: , :
162	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
163	instantiation	169, 165, 166	⊢
	: , : , :
164	instantiation	167, 168	⊢
	:
165	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
166	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
167	theorem		⊢
	proveit.numbers.negation.int_closure
168	instantiation	169, 170, 171	⊢
	: , : , :
169	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
170	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
171	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements