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*, 11*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	reference	92	⊢
3	reference	87	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	12	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	reference	63	⊢
8	reference	44	⊢
9	instantiation	90, 71, 13	⊢
	: , : , :
10	instantiation	14, 63	⊢
	:
11	instantiation	19, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	90, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
15	instantiation	19, 20, 21	⊢
	: , : , :
16	instantiation	41, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
18	instantiation	24, 25, 46, 26	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	27, 44, 28, 29, 30	⊢
	: , : , : , : , :
21	instantiation	51, 31	⊢
	: , : , :
22	instantiation	51, 32	⊢
	: , : , :
23	instantiation	62, 33	⊢
	:
24	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
25	instantiation	90, 66, 34	⊢
	: , : , :
26	instantiation	35, 36	⊢
	:
27	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
28	instantiation	90, 39, 37	⊢
	: , : , :
29	instantiation	90, 39, 38	⊢
	: , : , :
30	instantiation	90, 39, 40	⊢
	: , : , :
31	instantiation	41, 42, 43	⊢
	: , : , :
32	instantiation	53, 44	⊢
	:
33	instantiation	90, 71, 45	⊢
	: , : , :
34	instantiation	90, 76, 70	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
36	instantiation	90, 50, 46	⊢
	: , : , :
37	instantiation	90, 48, 47	⊢
	: , : , :
38	instantiation	90, 48, 49	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
40	instantiation	90, 50, 58	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.equality.equals_transitivity
42	instantiation	51, 52	⊢
	: , : , :
43	instantiation	53, 63	⊢
	:
44	instantiation	90, 71, 82	⊢
	: , : , :
45	instantiation	54, 82, 74, 55	⊢
	: , :
46	instantiation	56, 57, 58	⊢
	: , :
47	instantiation	90, 60, 59	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49	instantiation	90, 60, 61	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
51	axiom		⊢
	proveit.logic.equality.substitution
52	instantiation	62, 63	⊢
	:
53	theorem		⊢
	proveit.numbers.division.frac_one_denom
54	theorem		⊢
	proveit.numbers.division.div_real_closure
55	instantiation	64, 65	⊢
	: , :
56	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
57	instantiation	90, 66, 67	⊢
	: , : , :
58	instantiation	68, 74, 75	⊢
	:
59	instantiation	90, 69, 77	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61	instantiation	90, 69, 70	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
63	instantiation	90, 71, 72	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
65	instantiation	73, 81, 74, 75	⊢
	: , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
67	instantiation	90, 76, 77	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	instantiation	90, 85, 78	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
74	instantiation	79, 81, 82, 83	⊢
	: , : , :
75	instantiation	80, 81, 82, 83	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
78	instantiation	90, 88, 84	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
82	instantiation	90, 85, 86	⊢
	: , : , :
83	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
84	instantiation	90, 91, 87	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
86	instantiation	90, 88, 89	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
89	instantiation	90, 91, 92	⊢
	: , : , :
90	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements