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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 83, 8, 85, 9*, 10*, 11*	⊢
	: , : , : , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	12, 13, 14, 70, 15	⊢
	: , : , :
6	instantiation	16, 46, 17, 86, 47, 18, 49, 50, 51, 19	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
8	instantiation	20, 83	⊢
	:
9	instantiation	21, 53	⊢
	:
10	instantiation	22, 53, 42, 72	⊢
	: , :
11	instantiation	23, 24, 25	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
13	instantiation	26, 65	⊢
	:
14	instantiation	27, 29, 70, 30	⊢
	: , : , :
15	instantiation	28, 29, 70, 30	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.association
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
18	instantiation	31	⊢
	: , : , :
19	instantiation	55, 50	⊢
	:
20	theorem		⊢
	proveit.numbers.negation.int_closure
21	theorem		⊢
	proveit.numbers.division.frac_one_denom
22	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	32, 89, 33, 34, 35, 36	⊢
	: , : , : , :
25	instantiation	37, 53, 42, 38	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.real_closure
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	39, 62, 40*	⊢
	:
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
33	instantiation	54	⊢
	: , :
34	instantiation	54	⊢
	: , :
35	instantiation	41, 42	⊢
	:
36	instantiation	43, 53, 44*	⊢
	: , :
37	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
38	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
39	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
40	instantiation	45, 46, 89, 86, 47, 48, 49, 50, 51	⊢
	: , : , : , : , : , :
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	87, 57, 71	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
44	instantiation	52, 53	⊢
	:
45	theorem		⊢
	proveit.numbers.addition.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	54	⊢
	: , :
49	instantiation	87, 57, 64	⊢
	: , : , :
50	instantiation	87, 57, 65	⊢
	: , : , :
51	instantiation	55, 56	⊢
	:
52	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
53	instantiation	87, 57, 70	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
55	theorem		⊢
	proveit.numbers.negation.complex_closure
56	instantiation	73, 58, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	81, 60	⊢
	: , :
59	instantiation	61, 62	⊢
	:
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
61	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
62	instantiation	63, 64, 65	⊢
	: , :
63	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
64	instantiation	66, 67, 68	⊢
	: , :
65	instantiation	69, 70, 71, 72	⊢
	: , :
66	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
67	instantiation	73, 74, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
69	theorem		⊢
	proveit.numbers.division.div_real_closure
70	instantiation	87, 77, 76	⊢
	: , : , :
71	instantiation	87, 77, 78	⊢
	: , : , :
72	instantiation	79, 80	⊢
	:
73	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
74	instantiation	81, 82	⊢
	: , :
75	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
76	instantiation	87, 84, 83	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
78	instantiation	87, 84, 85	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
80	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
81	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
83	instantiation	87, 88, 86	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	87, 88, 89	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
87	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements