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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	60, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	57, 9	⊢
	: , :
6	instantiation	24, 45, 44, 10, 25*, 11*	⊢
	: , : , : , :
7	instantiation	12, 13	⊢
	: , : , :
8	instantiation	14, 117, 136, 15*	⊢
	: , : , : , :
9	instantiation	16, 17, 18, 19, 20, 21	⊢
	: , : , :
10	instantiation	138, 64, 22	⊢
	: , : , :
11	instantiation	23, 103, 121, 101, 81*	⊢
	: , : , :
12	axiom		⊢
	proveit.logic.equality.substitution
13	instantiation	24, 45, 44, 25*, 26*	⊢
	: , : , : , :
14	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
15	instantiation	60, 27, 28	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
17	instantiation	138, 131, 29	⊢
	: , : , :
18	instantiation	30, 33	⊢
	: , :
19	instantiation	138, 131, 31	⊢
	: , : , :
20	instantiation	32, 33, 34, 35, 36	⊢
	: , : , :
21	instantiation	82, 49	⊢
	:
22	instantiation	138, 90, 37	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
24	theorem		⊢
	proveit.numbers.division.prod_of_fracs
25	instantiation	109, 45	⊢
	:
26	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
27	instantiation	84, 137, 38, 39, 40, 41	⊢
	: , : , : , :
28	instantiation	42, 43, 44, 45, 46*, 47*	⊢
	: , : , :
29	instantiation	48, 50, 51	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
31	instantiation	138, 68, 49	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
33	instantiation	138, 131, 50	⊢
	: , : , :
34	instantiation	138, 131, 51	⊢
	: , : , :
35	instantiation	52, 53, 54, 55, 56	⊢
	: , : , :
36	instantiation	57, 58	⊢
	: , :
37	instantiation	138, 112, 59	⊢
	: , : , :
38	instantiation	107	⊢
	: , :
39	instantiation	107	⊢
	: , :
40	instantiation	60, 61, 62	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
42	theorem		⊢
	proveit.numbers.division.frac_cancel_left
43	instantiation	138, 64, 63	⊢
	: , : , :
44	instantiation	138, 64, 65	⊢
	: , : , :
45	instantiation	138, 123, 77	⊢
	: , : , :
46	instantiation	109, 66	⊢
	:
47	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
48	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
49	instantiation	104, 105, 67	⊢
	: , :
50	instantiation	138, 68, 83	⊢
	: , : , :
51	instantiation	69, 97, 70, 71	⊢
	: , :
52	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
53	instantiation	138, 72, 73	⊢
	: , : , :
54	instantiation	138, 74, 106	⊢
	: , : , :
55	instantiation	138, 74, 75	⊢
	: , : , :
56	instantiation	76, 120, 77, 78, 79, 80, 81*	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.ordering.relax_less
58	instantiation	82, 83	⊢
	:
59	instantiation	138, 126, 116	⊢
	: , : , :
60	axiom		⊢
	proveit.logic.equality.equals_transitivity
61	instantiation	84, 137, 85, 86, 87, 88	⊢
	: , : , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
63	instantiation	138, 90, 89	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
65	instantiation	138, 90, 91	⊢
	: , : , :
66	instantiation	138, 123, 92	⊢
	: , : , :
67	instantiation	138, 122, 93	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
69	theorem		⊢
	proveit.numbers.division.div_rational_closure
70	instantiation	138, 135, 94	⊢
	: , : , :
71	instantiation	95, 116	⊢
	:
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
73	instantiation	138, 96, 129	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
75	instantiation	138, 122, 116	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
77	instantiation	138, 131, 97	⊢
	: , : , :
78	instantiation	98, 99, 101	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
80	instantiation	100, 101	⊢
	:
81	instantiation	102, 103	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
83	instantiation	104, 105, 106	⊢
	: , :
84	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
85	instantiation	107	⊢
	: , :
86	instantiation	107	⊢
	: , :
87	instantiation	108, 110	⊢
	:
88	instantiation	109, 110	⊢
	:
89	instantiation	138, 112, 111	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
91	instantiation	138, 112, 113	⊢
	: , : , :
92	instantiation	138, 131, 114	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
94	instantiation	138, 115, 116	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
97	instantiation	138, 135, 117	⊢
	: , : , :
98	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
99	instantiation	118, 119	⊢
	: , :
100	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
101	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
102	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
103	instantiation	138, 123, 120	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
105	instantiation	138, 122, 121	⊢
	: , : , :
106	instantiation	138, 122, 127	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
108	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
109	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
110	instantiation	138, 123, 124	⊢
	: , : , :
111	instantiation	138, 126, 125	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
113	instantiation	138, 126, 127	⊢
	: , : , :
114	instantiation	138, 135, 128	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
116	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
117	instantiation	138, 139, 129	⊢
	: , : , :
118	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
120	instantiation	138, 131, 130	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
122	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
123	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
124	instantiation	138, 131, 132	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
126	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
127	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
128	instantiation	138, 139, 133	⊢
	: , : , :
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
130	instantiation	138, 135, 134	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	138, 135, 136	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
134	instantiation	138, 139, 137	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
136	instantiation	138, 139, 140	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
138	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
139	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
140	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements