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, 4	⊢
	: , : , : , :
1	reference	55	⊢
2	instantiation	5, 74, 102	⊢
	: , :
3	instantiation	67, 6	⊢
	: , :
4	instantiation	67, 7	⊢
	: , :
5	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
6	instantiation	8, 20, 74, 78, 9	⊢
	: , : , :
7	instantiation	33, 10, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
9	instantiation	39, 12, 13	⊢
	: , : , :
10	instantiation	33, 14, 15	⊢
	: , : , :
11	instantiation	33, 16, 17	⊢
	: , : , :
12	instantiation	33, 18, 19	⊢
	: , : , :
13	instantiation	76, 74, 20	⊢
	: , :
14	instantiation	69, 21	⊢
	: , : , :
15	instantiation	69, 22	⊢
	: , : , :
16	instantiation	33, 23, 24	⊢
	: , : , :
17	instantiation	25, 47, 145, 137, 49, 26, 53, 102, 63, 27*	⊢
	: , : , : , : , : , :
18	instantiation	46, 137, 145, 47, 28, 49, 74, 63, 78	⊢
	: , : , : , : , : , :
19	instantiation	29, 74, 78, 30	⊢
	: , : , :
20	instantiation	143, 123, 31	⊢
	: , : , :
21	instantiation	69, 44	⊢
	: , : , :
22	instantiation	69, 32	⊢
	: , : , :
23	instantiation	33, 34, 35	⊢
	: , : , :
24	instantiation	36, 47, 137, 145, 49, 37, 72, 53, 102, 63, 38	⊢
	: , : , : , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.addition.association
26	instantiation	64	⊢
	: , :
27	instantiation	39, 40, 41	⊢
	: , : , :
28	instantiation	64	⊢
	: , :
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
30	instantiation	50	⊢
	:
31	instantiation	42, 43, 88	⊢
	: , :
32	instantiation	69, 44	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	46, 47, 145, 137, 49, 48, 72, 53, 45	⊢
	: , : , : , : , : , :
35	instantiation	46, 145, 60, 47, 48, 61, 49, 72, 53, 62, 102, 63	⊢
	: , : , : , : , : , :
36	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
37	instantiation	64	⊢
	: , :
38	instantiation	50	⊢
	:
39	theorem		⊢
	proveit.logic.equality.sub_right_side_into
40	instantiation	51, 102, 116, 52	⊢
	: , : , :
41	instantiation	76, 102, 53	⊢
	: , :
42	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
43	instantiation	54, 86	⊢
	:
44	instantiation	55, 56, 57, 58	⊢
	: , : , : , :
45	instantiation	59, 60, 61, 62, 102, 63	⊢
	: , :
46	theorem		⊢
	proveit.numbers.addition.disassociation
47	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
48	instantiation	64	⊢
	: , :
49	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
50	axiom		⊢
	proveit.logic.equality.equals_reflexivity
51	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
52	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
53	instantiation	143, 123, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.negation.real_closure
55	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
56	instantiation	69, 66	⊢
	: , : , :
57	instantiation	67, 68	⊢
	: , :
58	instantiation	69, 70	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.add_complex_closure
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
61	instantiation	71	⊢
	: , : , :
62	instantiation	73, 72	⊢
	:
63	instantiation	73, 74	⊢
	:
64	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
65	instantiation	143, 130, 75	⊢
	: , : , :
66	instantiation	76, 77, 78	⊢
	: , :
67	theorem		⊢
	proveit.logic.equality.equals_reversal
68	instantiation	79, 116, 88, 87, 104	⊢
	: , : , :
69	axiom		⊢
	proveit.logic.equality.substitution
70	instantiation	80, 81, 82	⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
72	instantiation	83, 84, 85	⊢
	: , :
73	theorem		⊢
	proveit.numbers.negation.complex_closure
74	instantiation	143, 123, 86	⊢
	: , : , :
75	instantiation	143, 138, 136	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.addition.commutation
77	instantiation	143, 123, 87	⊢
	: , : , :
78	instantiation	143, 123, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
80	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
81	instantiation	143, 89, 90	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
83	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
84	instantiation	91, 102, 92, 93	⊢
	: , :
85	instantiation	143, 123, 94	⊢
	: , : , :
86	instantiation	143, 130, 95	⊢
	: , : , :
87	instantiation	96, 97, 133	⊢
	: , : , :
88	instantiation	143, 130, 98	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	143, 99, 100	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.division.div_complex_closure
92	instantiation	101, 116, 102	⊢
	: , :
93	instantiation	103, 104, 105	⊢
	: , : , :
94	instantiation	143, 130, 106	⊢
	: , : , :
95	instantiation	143, 138, 107	⊢
	: , : , :
96	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
97	instantiation	108, 109	⊢
	: , :
98	instantiation	143, 138, 110	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
100	instantiation	143, 111, 112	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
102	instantiation	143, 123, 113	⊢
	: , : , :
103	theorem		⊢
	proveit.logic.equality.sub_left_side_into
104	instantiation	114, 121	⊢
	:
105	instantiation	115, 116	⊢
	:
106	instantiation	143, 138, 117	⊢
	: , : , :
107	instantiation	143, 118, 119	⊢
	: , : , :
108	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
110	instantiation	141, 129	⊢
	:
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
112	instantiation	143, 120, 121	⊢
	: , : , :
113	instantiation	143, 130, 122	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
115	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
116	instantiation	143, 123, 124	⊢
	: , : , :
117	instantiation	125, 142, 126	⊢
	: , :
118	instantiation	127, 129, 128	⊢
	: , :
119	assumption		⊢
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
121	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
122	instantiation	143, 138, 129	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
124	instantiation	143, 130, 131	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
126	instantiation	143, 132, 133	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
128	instantiation	134, 135, 136	⊢
	: , :
129	instantiation	143, 144, 137	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
131	instantiation	143, 138, 142	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
133	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
134	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
135	instantiation	143, 139, 140	⊢
	: , : , :
136	instantiation	141, 142	⊢
	:
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
138	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
139	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
140	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_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.nat2
*equality replacement requirements