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	70	⊢
2	instantiation	4, 9, 10, 108, 11, 5, 90, 23, 15, 14, 16	⊢
	: , : , : , : , : , : , :
3	instantiation	70, 6, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	instantiation	19	⊢
	: , : , :
6	instantiation	8, 9, 115, 10, 11, 12, 13, 14, 90, 23, 15, 16	⊢
	: , : , : , : , : , :
7	instantiation	79, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	18	⊢
	: , :
13	instantiation	19	⊢
	: , : , :
14	instantiation	113, 96, 20	⊢
	: , : , :
15	instantiation	113, 96, 21	⊢
	: , : , :
16	instantiation	22, 23, 24	⊢
	: , :
17	instantiation	34, 25, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	instantiation	27, 73, 97, 28	⊢
	: , :
21	instantiation	29, 30, 31	⊢
	: , :
22	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
23	instantiation	113, 96, 32	⊢
	: , : , :
24	instantiation	113, 96, 33	⊢
	: , : , :
25	instantiation	34, 35, 36	⊢
	: , : , :
26	instantiation	37, 38, 39, 40	⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.division.div_real_closure
28	instantiation	41, 102	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
30	instantiation	42, 43	⊢
	:
31	instantiation	44, 45	⊢
	:
32	instantiation	113, 46, 47	⊢
	: , : , :
33	instantiation	113, 104, 48	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	49, 64, 50, 51	⊢
	: , : , : , : , :
36	instantiation	70, 52, 53	⊢
	: , : , :
37	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
38	instantiation	79, 54	⊢
	: , : , :
39	instantiation	79, 54	⊢
	: , : , :
40	instantiation	89, 64	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
42	theorem		⊢
	proveit.numbers.negation.real_closure
43	instantiation	55, 56, 57	⊢
	: , :
44	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
45	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
48	instantiation	113, 109, 58	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
50	instantiation	113, 60, 59	⊢
	: , : , :
51	instantiation	113, 60, 61	⊢
	: , : , :
52	instantiation	79, 62	⊢
	: , : , :
53	instantiation	79, 63	⊢
	: , : , :
54	instantiation	81, 64	⊢
	:
55	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
56	instantiation	113, 104, 65	⊢
	: , : , :
57	instantiation	113, 104, 66	⊢
	: , : , :
58	instantiation	106, 100	⊢
	:
59	instantiation	113, 68, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
61	instantiation	113, 68, 86	⊢
	: , : , :
62	instantiation	79, 69	⊢
	: , : , :
63	instantiation	70, 71, 72	⊢
	: , : , :
64	instantiation	113, 96, 73	⊢
	: , : , :
65	instantiation	113, 109, 74	⊢
	: , : , :
66	instantiation	113, 75, 76	⊢
	: , : , :
67	instantiation	113, 93, 77	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
69	instantiation	78, 90	⊢
	:
70	axiom		⊢
	proveit.logic.equality.equals_transitivity
71	instantiation	79, 80	⊢
	: , : , :
72	instantiation	81, 90	⊢
	:
73	instantiation	113, 104, 82	⊢
	: , : , :
74	instantiation	113, 83, 84	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
76	instantiation	85, 86, 87	⊢
	: , :
77	instantiation	113, 101, 88	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
79	axiom		⊢
	proveit.logic.equality.substitution
80	instantiation	89, 90	⊢
	:
81	theorem		⊢
	proveit.numbers.division.frac_one_denom
82	instantiation	113, 109, 100	⊢
	: , : , :
83	instantiation	91, 92, 107	⊢
	: , :
84	assumption		⊢
85	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
86	instantiation	113, 93, 94	⊢
	: , : , :
87	instantiation	106, 95	⊢
	:
88	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
89	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
90	instantiation	113, 96, 97	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
92	instantiation	98, 99, 100	⊢
	: , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
94	instantiation	113, 101, 102	⊢
	: , : , :
95	instantiation	113, 111, 103	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
97	instantiation	113, 104, 105	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
99	instantiation	106, 107	⊢
	:
100	instantiation	113, 114, 108	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
102	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
103	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
104	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
105	instantiation	113, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.negation.int_closure
107	instantiation	113, 111, 112	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
109	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
110	instantiation	113, 114, 115	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
112	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
113	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
114	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat2