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