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_abs_sum
2	reference	100	⊢
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	101, 11, 12	⊢
	: , : , :
7	instantiation	13	⊢
	: , :
8	instantiation	101, 83, 14	⊢
	: , : , :
9	instantiation	101, 83, 15	,  ⊢
	: , : , :
10	instantiation	16, 80, 17, 18*	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
12	instantiation	101, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	21, 22	⊢
	:
15	instantiation	101, 75, 23	,  ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
17	instantiation	101, 83, 24	,  ⊢
	: , : , :
18	instantiation	30, 25, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
20	instantiation	101, 27, 89	⊢
	: , : , :
21	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
22	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
23	instantiation	101, 38, 28	,  ⊢
	: , : , :
24	instantiation	101, 75, 29	,  ⊢
	: , : , :
25	instantiation	30, 31, 32	⊢
	: , : , :
26	instantiation	33, 34, 35, 36	⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
28	instantiation	37, 39	,  ⊢
	:
29	instantiation	101, 38, 39	,  ⊢
	: , : , :
30	theorem		⊢
	proveit.logic.equality.sub_right_side_into
31	instantiation	40, 54, 55, 41, 42	⊢
	: , : , : , : , :
32	instantiation	61, 43, 44	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
34	instantiation	70, 45	⊢
	: , : , :
35	instantiation	70, 46	⊢
	: , : , :
36	instantiation	79, 55	⊢
	:
37	theorem		⊢
	proveit.numbers.negation.rational_nonzero_closure
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
39	instantiation	47, 48, 58	,  ⊢
	: , :
40	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
41	instantiation	101, 50, 49	⊢
	: , : , :
42	instantiation	101, 50, 51	⊢
	: , : , :
43	instantiation	70, 52	⊢
	: , : , :
44	instantiation	70, 53	⊢
	: , : , :
45	instantiation	72, 54	⊢
	:
46	instantiation	72, 55	⊢
	:
47	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
48	instantiation	56, 76, 57	,  ⊢
	:
49	instantiation	101, 59, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
51	instantiation	101, 59, 60	⊢
	: , : , :
52	instantiation	61, 62, 63	⊢
	: , : , :
53	instantiation	70, 64	⊢
	: , : , :
54	instantiation	101, 83, 65	⊢
	: , : , :
55	instantiation	101, 83, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
57	assumption		⊢
58	instantiation	101, 68, 67	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
60	instantiation	101, 68, 69	⊢
	: , : , :
61	axiom		⊢
	proveit.logic.equality.equals_transitivity
62	instantiation	70, 71	⊢
	: , : , :
63	instantiation	72, 80	⊢
	:
64	instantiation	73, 80	⊢
	:
65	instantiation	101, 75, 74	⊢
	: , : , :
66	instantiation	101, 75, 76	⊢
	: , : , :
67	instantiation	101, 77, 89	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
69	instantiation	101, 77, 78	⊢
	: , : , :
70	axiom		⊢
	proveit.logic.equality.substitution
71	instantiation	79, 80	⊢
	:
72	theorem		⊢
	proveit.numbers.division.frac_one_denom
73	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
74	instantiation	101, 81, 96	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	101, 81, 82	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
79	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
80	instantiation	101, 83, 84	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
82	instantiation	101, 85, 86	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
84	instantiation	87, 88, 89	⊢
	: , : , :
85	instantiation	90, 91, 98	⊢
	: , :
86	assumption		⊢
87	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
88	instantiation	92, 93	⊢
	: , :
89	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
90	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
91	instantiation	94, 95, 96	⊢
	: , :
92	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
94	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
95	instantiation	97, 98	⊢
	:
96	instantiation	101, 99, 100	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.negation.int_closure
98	instantiation	101, 102, 103	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
101	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
102	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
103	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements