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	⊢
	: , : , :
1	reference	6	⊢
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 7	⊢
	: , : , :
5	instantiation	8, 18, 9*	⊢
	:
6	axiom		⊢
	proveit.logic.equality.substitution
7	instantiation	10, 11	⊢
	:
8	theorem		⊢
	proveit.numbers.absolute_value.abs_even
9	instantiation	12, 13, 14, 34, 35, 36, 15*, 16*	⊢
	: , :
10	theorem		⊢
	proveit.numbers.addition.elim_zero_left
11	instantiation	17, 18	⊢
	:
12	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
14	instantiation	19	⊢
	: , : , :
15	instantiation	21, 20	⊢
	:
16	instantiation	21, 22	⊢
	:
17	theorem		⊢
	proveit.numbers.negation.complex_closure
18	instantiation	23, 24, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	instantiation	26, 68	⊢
	:
21	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
22	instantiation	27, 28	⊢
	: , :
23	theorem		⊢
	proveit.logic.equality.sub_right_side_into
24	instantiation	66, 40, 29	⊢
	: , : , :
25	instantiation	30, 31, 68, 65, 32, 33, 34, 35, 36	⊢
	: , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
27	theorem		⊢
	proveit.numbers.ordering.relax_less
28	instantiation	37, 48	⊢
	:
29	instantiation	42, 38, 41	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.disassociation
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	39	⊢
	: , :
34	instantiation	66, 40, 55	⊢
	: , : , :
35	instantiation	66, 40, 43	⊢
	: , : , :
36	instantiation	66, 40, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
38	instantiation	42, 55, 43	⊢
	: , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	44, 45, 50, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
43	instantiation	66, 47, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
45	instantiation	49, 50	⊢
	:
46	instantiation	51, 52	⊢
	:
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49	theorem		⊢
	proveit.numbers.negation.real_closure
50	instantiation	53, 54, 55, 56	⊢
	: , :
51	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.division.div_real_closure
54	instantiation	66, 58, 57	⊢
	: , : , :
55	instantiation	66, 58, 59	⊢
	: , : , :
56	instantiation	60, 61	⊢
	:
57	instantiation	66, 63, 62	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	66, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
62	instantiation	66, 67, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	66, 67, 68	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
66	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements