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, 5, 6*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
2	reference	94	⊢
3	reference	9	⊢
4	instantiation	7, 10, 94	⊢
	: , :
5	instantiation	8, 9, 10, 94, 11, 12	⊢
	: , : , :
6	instantiation	53, 13, 14, 15	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
8	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
9	instantiation	127, 116, 16	⊢
	: , : , :
10	instantiation	127, 116, 17	⊢
	: , : , :
11	instantiation	18, 121, 34, 27	⊢
	: , : , :
12	instantiation	19, 126	⊢
	:
13	instantiation	36, 20, 21	⊢
	: , : , :
14	instantiation	39	⊢
	:
15	instantiation	65, 42	⊢
	: , :
16	instantiation	127, 124, 22	⊢
	: , : , :
17	instantiation	127, 124, 34	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
19	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
20	instantiation	67, 23	⊢
	: , : , :
21	instantiation	36, 24, 25	⊢
	: , : , :
22	instantiation	127, 26, 27	⊢
	: , : , :
23	instantiation	36, 28, 29	⊢
	: , : , :
24	instantiation	43, 46, 129, 126, 48, 30, 49, 78, 84	⊢
	: , : , : , : , : , :
25	instantiation	31, 84, 49, 32	⊢
	: , : , :
26	instantiation	33, 121, 34	⊢
	: , :
27	assumption		⊢
28	instantiation	67, 35	⊢
	: , : , :
29	instantiation	36, 37, 38	⊢
	: , : , :
30	instantiation	57	⊢
	: , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
32	instantiation	39	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
34	instantiation	40, 41, 110	⊢
	: , :
35	instantiation	67, 42	⊢
	: , : , :
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	43, 46, 129, 126, 48, 44, 49, 75, 84	⊢
	: , : , : , : , : , :
38	instantiation	45, 126, 129, 46, 47, 48, 49, 75, 84, 50*	⊢
	: , : , : , : , : , :
39	axiom		⊢
	proveit.logic.equality.equals_reflexivity
40	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
41	instantiation	127, 51, 52	⊢
	: , : , :
42	instantiation	53, 54, 55, 56	⊢
	: , : , : , :
43	theorem		⊢
	proveit.numbers.addition.disassociation
44	instantiation	57	⊢
	: , :
45	theorem		⊢
	proveit.numbers.addition.association
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	instantiation	57	⊢
	: , :
48	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
49	instantiation	58, 59, 60	⊢
	: , :
50	instantiation	61, 62, 63	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
52	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
53	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
54	instantiation	67, 64	⊢
	: , : , :
55	instantiation	65, 66	⊢
	: , :
56	instantiation	67, 68	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
58	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
59	instantiation	69, 84, 70, 71	⊢
	: , :
60	instantiation	127, 106, 72	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.equality.sub_right_side_into
62	instantiation	73, 84, 97, 74	⊢
	: , : , :
63	instantiation	76, 84, 75	⊢
	: , :
64	instantiation	76, 77, 78	⊢
	: , :
65	theorem		⊢
	proveit.logic.equality.equals_reversal
66	instantiation	79, 97, 91, 90, 86	⊢
	: , : , :
67	axiom		⊢
	proveit.logic.equality.substitution
68	instantiation	80, 81, 82	⊢
	: , :
69	theorem		⊢
	proveit.numbers.division.div_complex_closure
70	instantiation	83, 97, 84	⊢
	: , :
71	instantiation	85, 86, 87	⊢
	: , : , :
72	instantiation	127, 116, 88	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
74	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
75	instantiation	127, 106, 89	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.addition.commutation
77	instantiation	127, 106, 90	⊢
	: , : , :
78	instantiation	127, 106, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
80	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
81	instantiation	127, 92, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
83	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
84	instantiation	127, 106, 94	⊢
	: , : , :
85	theorem		⊢
	proveit.logic.equality.sub_left_side_into
86	instantiation	95, 123	⊢
	:
87	instantiation	96, 97	⊢
	:
88	instantiation	127, 124, 98	⊢
	: , : , :
89	instantiation	127, 116, 99	⊢
	: , : , :
90	instantiation	100, 101, 119	⊢
	: , : , :
91	instantiation	127, 116, 102	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
93	instantiation	127, 103, 104	⊢
	: , : , :
94	instantiation	127, 116, 105	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
96	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
97	instantiation	127, 106, 107	⊢
	: , : , :
98	instantiation	108, 125, 109	⊢
	: , :
99	instantiation	127, 124, 110	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
101	instantiation	111, 112	⊢
	: , :
102	instantiation	127, 124, 113	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
104	instantiation	127, 114, 115	⊢
	: , : , :
105	instantiation	127, 124, 121	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
107	instantiation	127, 116, 117	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
109	instantiation	127, 118, 119	⊢
	: , : , :
110	instantiation	120, 125	⊢
	:
111	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
112	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
113	instantiation	120, 121	⊢
	:
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
115	instantiation	127, 122, 123	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
117	instantiation	127, 124, 125	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
119	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
120	theorem		⊢
	proveit.numbers.negation.int_closure
121	instantiation	127, 128, 126	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
124	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
125	instantiation	127, 128, 129	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
127	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements