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	modus ponens	1, 2	⊢
1	instantiation	3, 99	⊢
	: , : , : , : , : , :
2	generalization	4	⊢
3	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
4	instantiation	5, 6	⊢
	: , : , :
5	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
6	deduction	7	⊢
7	instantiation	80, 8, 9	⊢
	: , : , :
8	instantiation	52, 10	⊢
	: , : , :
9	instantiation	11, 38, 12, 30, 13*	⊢
	: , : , :
10	instantiation	14, 15, 16, 17, 18, 19	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
12	instantiation	20, 57	⊢
	:
13	instantiation	80, 21, 22	⊢
	: , : , :
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
16	instantiation	114	⊢
	: , :
17	instantiation	114	⊢
	: , :
18	instantiation	52, 23	⊢
	: , : , :
19	instantiation	24	⊢
	:
20	theorem		⊢
	proveit.numbers.negation.complex_closure
21	instantiation	52, 25	⊢
	: , : , :
22	instantiation	26, 27	⊢
	:
23	instantiation	52, 28	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	instantiation	29, 57, 30, 31	⊢
	: , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
27	instantiation	141, 118, 32	⊢
	: , : , :
28	instantiation	80, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
30	instantiation	89, 35, 36	⊢
	: , : , :
31	instantiation	69, 93, 143, 102, 37, 103, 106, 107, 112, 113, 105	⊢
	: , : , : , : , : , : , :
32	instantiation	141, 121, 38	⊢
	: , : , :
33	instantiation	52, 39	⊢
	: , : , :
34	instantiation	80, 40, 41	⊢
	: , : , :
35	instantiation	111, 92, 42	⊢
	: , :
36	instantiation	80, 43, 44	⊢
	: , : , :
37	instantiation	108	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
39	instantiation	101, 70, 128, 102, 71, 45, 103, 106, 107, 112, 113, 75, 105	⊢
	: , : , : , : , : , :
40	instantiation	80, 46, 47	⊢
	: , : , :
41	instantiation	48, 57	⊢
	:
42	instantiation	89, 49, 50	⊢
	: , : , :
43	instantiation	101, 143, 93, 102, 51, 103, 92, 112, 105, 113	⊢
	: , : , : , : , : , :
44	instantiation	101, 102, 128, 93, 103, 94, 51, 106, 107, 112, 105, 113	⊢
	: , : , : , : , : , :
45	instantiation	114	⊢
	: , :
46	instantiation	52, 53	⊢
	: , : , :
47	instantiation	54, 55, 56, 57, 58*	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.division.frac_one_denom
49	instantiation	111, 59, 113	⊢
	: , :
50	instantiation	101, 102, 128, 143, 103, 60, 112, 105, 113	⊢
	: , : , : , : , : , :
51	instantiation	108	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.substitution
53	instantiation	80, 61, 62	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.division.frac_cancel_left
55	instantiation	141, 64, 63	⊢
	: , : , :
56	instantiation	141, 64, 65	⊢
	: , : , :
57	instantiation	89, 66, 67	⊢
	: , : , :
58	instantiation	68, 75	⊢
	:
59	instantiation	111, 112, 105	⊢
	: , :
60	instantiation	114	⊢
	: , :
61	instantiation	69, 102, 70, 143, 103, 71, 106, 107, 112, 113, 75, 105	⊢
	: , : , : , : , : , : , :
62	instantiation	72, 143, 73, 102, 74, 103, 75, 106, 107, 112, 113, 105	⊢
	: , : , : , : , : , :
63	instantiation	141, 77, 76	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
65	instantiation	141, 77, 78	⊢
	: , : , :
66	instantiation	111, 92, 79	⊢
	: , :
67	instantiation	80, 81, 82	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
69	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
71	instantiation	83	⊢
	: , : , : , :
72	theorem		⊢
	proveit.numbers.multiplication.association
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
74	instantiation	84	⊢
	: , : , : , : , :
75	instantiation	141, 118, 85	⊢
	: , : , :
76	instantiation	141, 87, 86	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	141, 87, 88	⊢
	: , : , :
79	instantiation	89, 90, 91	⊢
	: , : , :
80	axiom		⊢
	proveit.logic.equality.equals_transitivity
81	instantiation	101, 143, 93, 102, 95, 103, 92, 112, 113, 105	⊢
	: , : , : , : , : , :
82	instantiation	101, 102, 128, 93, 103, 94, 95, 106, 107, 112, 113, 105	⊢
	: , : , : , : , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
84	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
85	instantiation	96, 97, 138	⊢
	: , : , :
86	instantiation	141, 98, 138	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
88	instantiation	141, 98, 99	⊢
	: , : , :
89	theorem		⊢
	proveit.logic.equality.sub_right_side_into
90	instantiation	111, 100, 105	⊢
	: , :
91	instantiation	101, 102, 128, 143, 103, 104, 112, 113, 105	⊢
	: , : , : , : , : , :
92	instantiation	111, 106, 107	⊢
	: , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
94	instantiation	114	⊢
	: , :
95	instantiation	108	⊢
	: , : , :
96	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
97	instantiation	109, 110	⊢
	: , :
98	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
99	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
100	instantiation	111, 112, 113	⊢
	: , :
101	theorem		⊢
	proveit.numbers.multiplication.disassociation
102	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
103	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
104	instantiation	114	⊢
	: , :
105	instantiation	141, 118, 115	⊢
	: , : , :
106	instantiation	141, 118, 116	⊢
	: , : , :
107	instantiation	141, 118, 117	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
109	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
111	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
112	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
113	instantiation	141, 118, 119	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
115	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
116	instantiation	141, 123, 120	⊢
	: , : , :
117	instantiation	141, 121, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
119	instantiation	141, 123, 124	⊢
	: , : , :
120	instantiation	141, 126, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
124	instantiation	141, 126, 127	⊢
	: , : , :
125	instantiation	141, 142, 128	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
127	instantiation	141, 129, 130	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
129	instantiation	131, 132, 133	⊢
	: , :
130	assumption		⊢
131	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
132	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
133	instantiation	134, 135, 136	⊢
	: , :
134	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
135	instantiation	141, 137, 138	⊢
	: , : , :
136	instantiation	139, 140	⊢
	:
137	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
138	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
139	theorem		⊢
	proveit.numbers.negation.int_closure
140	instantiation	141, 142, 143	⊢
	: , : , :
141	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
142	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
143	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements