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, 8, 9	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	reference	127	⊢
3	reference	137	⊢
4	reference	80	⊢
5	instantiation	10	⊢
	: , :
6	reference	81	⊢
7	instantiation	135, 50, 11	⊢
	: , : , :
8	modus ponens	12, 13	⊢
9	modus ponens	14, 15	⊢
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	instantiation	28, 29, 16, 17	⊢
	: , :
12	instantiation	19	⊢
	: , : , :
13	generalization	18	⊢
14	instantiation	19	⊢
	: , : , :
15	generalization	20	⊢
16	instantiation	135, 64, 21	⊢
	: , : , :
17	instantiation	82, 22	⊢
	:
18	instantiation	135, 50, 23	,  ⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
20	instantiation	135, 50, 24	,  ⊢
	: , : , :
21	instantiation	135, 75, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
23	instantiation	28, 29, 26, 27	,  ⊢
	: , :
24	instantiation	28, 29, 30, 31	,  ⊢
	: , :
25	instantiation	135, 136, 32	⊢
	: , : , :
26	instantiation	35, 48, 137	,  ⊢
	: , :
27	instantiation	36, 33	,  ⊢
	:
28	theorem		⊢
	proveit.numbers.division.div_real_closure
29	instantiation	135, 64, 34	⊢
	: , : , :
30	instantiation	35, 51, 137	,  ⊢
	: , :
31	instantiation	36, 37	,  ⊢
	:
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
33	instantiation	39, 38, 41	,  ⊢
	: , :
34	instantiation	135, 75, 124	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_if_in_complex_nonzero
37	instantiation	39, 40, 41	,  ⊢
	: , :
38	instantiation	44, 42, 43	,  ⊢
	:
39	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
40	instantiation	44, 45, 46	,  ⊢
	:
41	instantiation	135, 50, 47	⊢
	: , : , :
42	instantiation	135, 50, 48	,  ⊢
	: , : , :
43	instantiation	52, 49	,  ⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
45	instantiation	135, 50, 51	,  ⊢
	: , : , :
46	instantiation	52, 53	,  ⊢
	: , :
47	instantiation	135, 64, 54	⊢
	: , : , :
48	instantiation	57, 55, 59	,  ⊢
	: , :
49	instantiation	60, 56	,  ⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	57, 58, 59	,  ⊢
	: , :
52	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
53	instantiation	60, 61	,  ⊢
	: , :
54	instantiation	135, 75, 134	⊢
	: , : , :
55	instantiation	135, 64, 62	,  ⊢
	: , : , :
56	instantiation	68, 69, 72, 63	,  ⊢
	: , :
57	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
58	instantiation	135, 64, 65	,  ⊢
	: , : , :
59	instantiation	66, 67	⊢
	:
60	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
61	instantiation	68, 69, 93, 70	,  ⊢
	: , :
62	instantiation	135, 75, 72	,  ⊢
	: , : , :
63	instantiation	71, 72, 73, 74	,  ⊢
	: , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
65	instantiation	135, 75, 93	,  ⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.real_closure
67	instantiation	76, 77, 78	⊢
	: , :
68	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_not_eq_nonzeroInt
69	instantiation	79, 80, 127, 81	⊢
	: , : , : , : , :
70	instantiation	82, 83	,  ⊢
	:
71	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_int
72	instantiation	135, 84, 98	,  ⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
74	instantiation	85, 86, 87	,  ⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
77	instantiation	88, 89, 90	⊢
	: , : , :
78	instantiation	91, 92	⊢
	:
79	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
80	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
81	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
82	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
83	instantiation	115, 93, 94	,  ⊢
	:
84	instantiation	122, 96, 97	⊢
	: , :
85	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
86	instantiation	95, 96, 97, 98	,  ⊢
	: , : , :
87	instantiation	99, 100	⊢
	:
88	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
89	instantiation	101, 102	⊢
	: , :
90	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
91	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
92	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
93	instantiation	135, 103, 111	,  ⊢
	: , : , :
94	instantiation	119, 104, 105	,  ⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
96	instantiation	128, 106, 124	⊢
	: , :
97	instantiation	133, 110	⊢
	:
98	assumption		⊢
99	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
100	instantiation	107, 109	⊢
	:
101	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
103	instantiation	122, 110, 129	⊢
	: , :
104	instantiation	108, 109	⊢
	:
105	instantiation	123, 110, 129, 111	,  ⊢
	: , : , :
106	instantiation	133, 129	⊢
	:
107	theorem		⊢
	proveit.numbers.negation.int_neg_closure
108	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
109	instantiation	112, 113, 114	⊢
	: , :
110	instantiation	128, 116, 124	⊢
	: , :
111	assumption		⊢
112	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
113	instantiation	115, 116, 117	⊢
	:
114	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
115	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
116	instantiation	135, 118, 126	⊢
	: , : , :
117	instantiation	119, 120, 121	⊢
	: , : , :
118	instantiation	122, 124, 125	⊢
	: , :
119	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
120	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
121	instantiation	123, 124, 125, 126	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
123	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
124	instantiation	135, 136, 127	⊢
	: , : , :
125	instantiation	128, 129, 130	⊢
	: , :
126	assumption		⊢
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
128	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
129	instantiation	135, 131, 132	⊢
	: , : , :
130	instantiation	133, 134	⊢
	:
131	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
132	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
133	theorem		⊢
	proveit.numbers.negation.int_closure
134	instantiation	135, 136, 137	⊢
	: , : , :
135	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat2