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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	instantiation	8, 66	⊢
	:
3	instantiation	9, 11, 71, 12	⊢
	: , : , :
4	reference	71	⊢
5	instantiation	10, 11, 71, 12	⊢
	: , : , :
6	instantiation	30, 13, 14	⊢
	: , : , :
7	instantiation	15, 84, 16, 86, 17*, 18*, 19*	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.negation.real_closure
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	instantiation	20, 62, 21*	⊢
	:
13	instantiation	33, 34, 22, 87, 35, 23, 37, 40, 38, 24	⊢
	: , : , : , : , : , :
14	instantiation	25, 87, 34, 35, 37, 40, 38, 26	⊢
	: , : , : , : , : , : , : , :
15	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
16	instantiation	27, 84	⊢
	:
17	instantiation	28, 59	⊢
	:
18	instantiation	29, 59, 53, 73	⊢
	: , :
19	instantiation	30, 31, 32	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.rounding.real_minus_floor_interval
21	instantiation	33, 34, 90, 87, 35, 36, 37, 40, 38	⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
23	instantiation	39	⊢
	: , : , :
24	instantiation	49, 40	⊢
	:
25	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
26	instantiation	41	⊢
	:
27	theorem		⊢
	proveit.numbers.negation.int_closure
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
30	axiom		⊢
	proveit.logic.equality.equals_transitivity
31	instantiation	42, 90, 43, 44, 45, 46	⊢
	: , : , : , :
32	instantiation	47, 59, 53, 48	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.disassociation
34	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	51	⊢
	: , :
37	instantiation	88, 63, 65	⊢
	: , : , :
38	instantiation	49, 50	⊢
	:
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
40	instantiation	88, 63, 66	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.equality.equals_reflexivity
42	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
43	instantiation	51	⊢
	: , :
44	instantiation	51	⊢
	: , :
45	instantiation	52, 53	⊢
	:
46	instantiation	54, 59, 55*	⊢
	: , :
47	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	theorem		⊢
	proveit.numbers.negation.complex_closure
50	instantiation	74, 56, 57	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
53	instantiation	88, 63, 72	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
55	instantiation	58, 59	⊢
	:
56	instantiation	82, 60	⊢
	: , :
57	instantiation	61, 62	⊢
	:
58	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
59	instantiation	88, 63, 71	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.int_within_complex
61	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
62	instantiation	64, 65, 66	⊢
	: , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
65	instantiation	67, 68, 69	⊢
	: , :
66	instantiation	70, 71, 72, 73	⊢
	: , :
67	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
68	instantiation	74, 75, 76	⊢
	: , : , :
69	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
70	theorem		⊢
	proveit.numbers.division.div_real_closure
71	instantiation	88, 78, 77	⊢
	: , : , :
72	instantiation	88, 78, 79	⊢
	: , : , :
73	instantiation	80, 81	⊢
	:
74	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
75	instantiation	82, 83	⊢
	: , :
76	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
77	instantiation	88, 85, 84	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	88, 85, 86	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
82	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
84	instantiation	88, 89, 87	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
86	instantiation	88, 89, 90	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
88	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements