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