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*, 7*	⊢
	: , : , :
1	reference	21	⊢
2	reference	48	⊢
3	instantiation	75, 114, 22	⊢
	: , :
4	instantiation	61, 64, 114	⊢
	: , :
5	instantiation	8, 9, 10, 133, 11, 12	⊢
	: , : , :
6	instantiation	91, 13	⊢
	: , :
7	instantiation	31, 14, 15, 16	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.ordering.less_add_right_weak_int
9	instantiation	134, 135, 17	⊢
	: , : , :
10	instantiation	134, 135, 18	⊢
	: , : , :
11	instantiation	19, 114, 22, 111, 69, 20	⊢
	: , : , :
12	instantiation	21, 63, 22, 58, 23, 24*, 25*	⊢
	: , : , :
13	instantiation	31, 26, 27, 28	⊢
	: , : , : , :
14	instantiation	86, 94, 136, 126, 95, 30, 51, 109, 29	⊢
	: , : , : , : , : , :
15	instantiation	86, 136, 94, 30, 89, 95, 51, 109, 90, 97	⊢
	: , : , : , : , : , :
16	instantiation	31, 32, 33, 34	⊢
	: , : , : , :
17	instantiation	35, 136, 94	⊢
	: , :
18	instantiation	35, 136, 36	⊢
	: , :
19	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
20	instantiation	37, 38	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
23	instantiation	39, 102	⊢
	:
24	instantiation	40, 41, 42	⊢
	: , : , :
25	instantiation	107, 109, 108, 43, 44	⊢
	: , : , :
26	instantiation	45, 104, 108	⊢
	: , :
27	instantiation	46	⊢
	:
28	instantiation	91, 47	⊢
	: , :
29	instantiation	134, 113, 48	⊢
	: , : , :
30	instantiation	105	⊢
	: , :
31	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
32	instantiation	49, 126, 51, 109, 90, 97	⊢
	: , : , : , : , : , : , :
33	instantiation	53, 94, 136, 95, 50, 96, 51, 90, 109, 97, 52*	⊢
	: , : , : , : , : , :
34	instantiation	53, 126, 136, 94, 96, 95, 104, 109, 97, 99*	⊢
	: , : , : , : , : , :
35	theorem		⊢
	proveit.numbers.multiplication.mult_nat_closure_bin
36	instantiation	54, 119, 55	⊢
	:
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	56, 97	⊢
	:
42	instantiation	57, 97, 87	⊢
	: , :
43	instantiation	134, 113, 58	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
45	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
46	axiom		⊢
	proveit.logic.equality.equals_reflexivity
47	instantiation	78, 59, 60	⊢
	: , : , :
48	instantiation	61, 62, 63	⊢
	: , :
49	theorem		⊢
	proveit.numbers.addition.leftward_commutation
50	instantiation	105	⊢
	: , :
51	instantiation	134, 113, 64	⊢
	: , : , :
52	instantiation	78, 65, 66, 67*	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.association
54	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
55	instantiation	68, 69	⊢
	: , :
56	theorem		⊢
	proveit.numbers.addition.elim_zero_right
57	theorem		⊢
	proveit.numbers.addition.commutation
58	instantiation	134, 117, 70	⊢
	: , : , :
59	instantiation	98, 71	⊢
	: , : , :
60	instantiation	78, 72, 73	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
62	instantiation	74, 111	⊢
	:
63	instantiation	74, 112	⊢
	:
64	instantiation	75, 114, 111	⊢
	: , :
65	instantiation	98, 76	⊢
	: , : , :
66	instantiation	91, 77	⊢
	: , :
67	instantiation	78, 79, 80	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.ordering.relax_less
69	instantiation	81, 82, 83	⊢
	: , : , :
70	instantiation	134, 120, 84	⊢
	: , : , :
71	instantiation	85, 109	⊢
	:
72	instantiation	86, 126, 136, 94, 89, 95, 87, 90, 97	⊢
	: , : , : , : , : , :
73	instantiation	88, 94, 136, 95, 89, 90, 97	⊢
	: , : , : , :
74	theorem		⊢
	proveit.numbers.negation.real_closure
75	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
76	instantiation	91, 92	⊢
	: , :
77	instantiation	93, 94, 136, 126, 95, 96, 109, 97, 104	⊢
	: , : , : , : , : , :
78	axiom		⊢
	proveit.logic.equality.equals_transitivity
79	instantiation	98, 99	⊢
	: , : , :
80	instantiation	100, 104	⊢
	:
81	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
82	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
83	instantiation	101, 124, 125, 122	⊢
	: , : , :
84	instantiation	134, 135, 102	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
86	theorem		⊢
	proveit.numbers.addition.disassociation
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
88	theorem		⊢
	proveit.numbers.addition.elim_zero_any
89	instantiation	105	⊢
	: , :
90	instantiation	106, 104	⊢
	:
91	theorem		⊢
	proveit.logic.equality.equals_reversal
92	instantiation	103, 104	⊢
	:
93	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
94	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
95	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
96	instantiation	105	⊢
	: , :
97	instantiation	106, 108	⊢
	:
98	axiom		⊢
	proveit.logic.equality.substitution
99	instantiation	107, 108, 109, 110	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
101	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
103	theorem		⊢
	proveit.numbers.negation.mult_neg_one_left
104	instantiation	134, 113, 111	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
106	theorem		⊢
	proveit.numbers.negation.complex_closure
107	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
108	instantiation	134, 113, 112	⊢
	: , : , :
109	instantiation	134, 113, 114	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
111	instantiation	134, 117, 115	⊢
	: , : , :
112	instantiation	134, 117, 116	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
114	instantiation	134, 117, 118	⊢
	: , : , :
115	instantiation	134, 120, 119	⊢
	: , : , :
116	instantiation	134, 120, 124	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
118	instantiation	134, 120, 133	⊢
	: , : , :
119	instantiation	134, 121, 122	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	instantiation	123, 124, 125	⊢
	: , :
122	assumption		⊢
123	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
124	instantiation	134, 135, 126	⊢
	: , : , :
125	instantiation	127, 128, 129	⊢
	: , :
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
127	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
128	instantiation	134, 130, 131	⊢
	: , : , :
129	instantiation	132, 133	⊢
	:
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
131	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
132	theorem		⊢
	proveit.numbers.negation.int_closure
133	instantiation	134, 135, 136	⊢
	: , : , :
134	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
136	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements