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	43	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	48, 147, 157, 49, 6, 50, 22, 7, 27, 8*	⊢
	: , : , : , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	43, 9, 10	⊢
	: , : , :
6	instantiation	75	⊢
	: , :
7	instantiation	11, 81, 69	⊢
	: , :
8	instantiation	43, 12, 13	⊢
	: , : , :
9	instantiation	14, 147, 157, 49, 15, 50, 69, 27	⊢
	: , : , : , : , : , :
10	instantiation	43, 16, 17	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
12	instantiation	18, 147, 157, 49, 19, 50, 22, 81, 69	⊢
	: , : , : , : , : , :
13	instantiation	20, 49, 157, 147, 50, 21, 22, 81, 69, 23*	⊢
	: , : , : , : , : , :
14	theorem		⊢
	proveit.numbers.addition.disassociation
15	instantiation	75	⊢
	: , :
16	instantiation	24, 147, 49, 50, 69, 27	⊢
	: , : , : , : , : , : , :
17	instantiation	25, 49, 157, 147, 50, 26, 69, 27, 28*	⊢
	: , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.multiplication.disassociation
19	instantiation	75	⊢
	: , :
20	theorem		⊢
	proveit.numbers.multiplication.association
21	instantiation	75	⊢
	: , :
22	instantiation	155, 89, 29	⊢
	: , : , :
23	instantiation	30, 64, 81, 31, 32, 33*, 34*	⊢
	: , : , : , :
24	theorem		⊢
	proveit.numbers.addition.leftward_commutation
25	theorem		⊢
	proveit.numbers.addition.association
26	instantiation	75	⊢
	: , :
27	instantiation	155, 89, 35	⊢
	: , : , :
28	instantiation	36, 37, 38*	⊢
	: , :
29	instantiation	155, 109, 39	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.prod_of_fracs
31	instantiation	155, 78, 40	⊢
	: , : , :
32	instantiation	155, 78, 41	⊢
	: , : , :
33	instantiation	42, 81	⊢
	:
34	instantiation	43, 44, 45	⊢
	: , : , :
35	instantiation	98, 99, 46, 47	⊢
	: , :
36	theorem		⊢
	proveit.logic.equality.equals_reversal
37	instantiation	48, 49, 157, 147, 50, 51, 64, 69, 52*	⊢
	: , : , : , : , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
39	instantiation	155, 53, 54	⊢
	: , : , :
40	instantiation	155, 88, 55	⊢
	: , : , :
41	instantiation	155, 88, 56	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.division.frac_one_denom
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	57, 157, 58, 59, 60, 61	⊢
	: , : , : , :
45	instantiation	62, 63, 64, 65*, 66*	⊢
	: , : , :
46	instantiation	104, 67, 157	⊢
	: , :
47	instantiation	106, 68, 108	⊢
	: , :
48	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
49	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
50	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
51	instantiation	75	⊢
	: , :
52	instantiation	76, 69	⊢
	:
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
54	instantiation	70, 71, 72	⊢
	: , :
55	instantiation	155, 112, 73	⊢
	: , : , :
56	instantiation	155, 112, 74	⊢
	: , : , :
57	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
58	instantiation	75	⊢
	: , :
59	instantiation	75	⊢
	: , :
60	instantiation	76, 81	⊢
	:
61	instantiation	80, 77	⊢
	:
62	theorem		⊢
	proveit.numbers.division.frac_cancel_left
63	instantiation	155, 78, 79	⊢
	: , : , :
64	instantiation	155, 89, 99	⊢
	: , : , :
65	instantiation	80, 81	⊢
	:
66	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
67	instantiation	155, 109, 82	⊢
	: , : , :
68	instantiation	155, 112, 83	⊢
	: , : , :
69	instantiation	155, 89, 84	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
71	instantiation	155, 85, 141	⊢
	: , : , :
72	instantiation	155, 85, 86	⊢
	: , : , :
73	instantiation	155, 116, 86	⊢
	: , : , :
74	instantiation	155, 116, 141	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
76	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
77	instantiation	155, 89, 87	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
79	instantiation	155, 88, 108	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
81	instantiation	155, 89, 90	⊢
	: , : , :
82	instantiation	155, 114, 132	⊢
	: , : , :
83	instantiation	155, 116, 129	⊢
	: , : , :
84	modus ponens	91, 92	⊢
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
87	instantiation	155, 109, 93	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
90	instantiation	155, 109, 94	⊢
	: , : , :
91	instantiation	95	⊢
	: , : , :
92	generalization	96	⊢
93	instantiation	155, 114, 97	⊢
	: , : , :
94	instantiation	155, 114, 154	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.summation.summation_real_closure
96	instantiation	98, 99, 100, 101	,  ⊢
	: , :
97	instantiation	155, 156, 102	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.division.div_real_closure
99	instantiation	155, 109, 103	⊢
	: , : , :
100	instantiation	104, 105, 157	,  ⊢
	: , :
101	instantiation	106, 107, 108	,  ⊢
	: , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
103	instantiation	155, 114, 144	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
105	instantiation	155, 109, 110	,  ⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
107	instantiation	155, 112, 111	,  ⊢
	: , : , :
108	instantiation	155, 112, 113	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
110	instantiation	155, 114, 118	,  ⊢
	: , : , :
111	instantiation	155, 116, 115	,  ⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
113	instantiation	155, 116, 117	⊢
	: , : , :
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
115	instantiation	131, 118, 119	,  ⊢
	:
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
118	instantiation	155, 120, 127	,  ⊢
	: , : , :
119	instantiation	137, 121, 122	,  ⊢
	: , : , :
120	instantiation	142, 125, 126	⊢
	: , :
121	instantiation	123, 124	⊢
	:
122	instantiation	143, 125, 126, 127	,  ⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
124	instantiation	128, 129, 141	⊢
	: , :
125	instantiation	148, 132, 144	⊢
	: , :
126	instantiation	148, 149, 130	⊢
	: , :
127	assumption		⊢
128	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
129	instantiation	131, 132, 133	⊢
	:
130	instantiation	155, 134, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
132	instantiation	155, 136, 146	⊢
	: , : , :
133	instantiation	137, 138, 139	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
135	instantiation	140, 141	⊢
	:
136	instantiation	142, 144, 145	⊢
	: , :
137	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
138	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
139	instantiation	143, 144, 145, 146	⊢
	: , : , :
140	theorem		⊢
	proveit.numbers.negation.int_neg_closure
141	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
142	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
143	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
144	instantiation	155, 156, 147	⊢
	: , : , :
145	instantiation	148, 149, 150	⊢
	: , :
146	assumption		⊢
147	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
148	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
149	instantiation	155, 151, 152	⊢
	: , : , :
150	instantiation	153, 154	⊢
	:
151	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
152	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
153	theorem		⊢
	proveit.numbers.negation.int_closure
154	instantiation	155, 156, 157	⊢
	: , : , :
155	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
156	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
157	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements