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