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