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	deduction	1	⊢
1	instantiation	2, 3, 4, 74, 68, 5, 6	,  ⊢
	: , :
2	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
4	instantiation	7	⊢
	: , : , : , :
5	instantiation	86, 113, 87, 8, 88, 90	⊢
	: , : , : , : , :
6	instantiation	9, 38, 55, 74, 10	,  ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
8	instantiation	99	⊢
	: , :
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
10	instantiation	11, 12, 13	,  ⊢
	: , :
11	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
12	instantiation	28, 85, 38, 29, 14, 32, 15*, 33*	,  ⊢
	: , : , :
13	instantiation	16, 17, 18	,  ⊢
	: , : , :
14	instantiation	19, 79, 80, 68	,  ⊢
	: , : , :
15	instantiation	20, 73, 52	⊢
	:
16	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
17	instantiation	21, 22, 23	,  ⊢
	: , : , :
18	instantiation	24, 55, 25, 38, 26, 27*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
20	theorem		⊢
	proveit.numbers.division.frac_zero_numer
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	28, 85, 29, 30, 31, 32, 33*	,  ⊢
	: , : , :
23	instantiation	34, 73, 43, 52, 35*	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
25	instantiation	36, 39	⊢
	:
26	instantiation	37, 38, 39, 40, 41*	⊢
	: , :
27	instantiation	42, 43	⊢
	:
28	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
29	instantiation	114, 97, 44	,  ⊢
	: , : , :
30	instantiation	114, 97, 45	⊢
	: , : , :
31	instantiation	46, 79, 80, 68	,  ⊢
	: , : , :
32	instantiation	47, 102	⊢
	:
33	instantiation	48, 49, 50	,  ⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
35	instantiation	51, 73, 52	⊢
	:
36	theorem		⊢
	proveit.numbers.negation.real_closure
37	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
39	instantiation	114, 97, 53	⊢
	: , : , :
40	instantiation	54, 65	⊢
	:
41	theorem		⊢
	proveit.numbers.negation.negated_zero
42	theorem		⊢
	proveit.numbers.addition.elim_zero_right
43	instantiation	114, 84, 55	⊢
	: , : , :
44	instantiation	114, 105, 56	,  ⊢
	: , : , :
45	instantiation	114, 105, 80	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	57, 58, 59, 62, 60*	,  ⊢
	: , : , :
50	instantiation	61, 62	⊢
	:
51	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
52	instantiation	63, 102	⊢
	:
53	instantiation	114, 64, 65	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
55	instantiation	114, 97, 66	⊢
	: , : , :
56	instantiation	114, 67, 68	,  ⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.division.frac_cancel_left
58	instantiation	114, 70, 69	⊢
	: , : , :
59	instantiation	114, 70, 71	⊢
	: , : , :
60	instantiation	72, 73	⊢
	:
61	theorem		⊢
	proveit.numbers.division.frac_one_denom
62	instantiation	114, 84, 74	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
65	instantiation	75, 76, 77	⊢
	: , :
66	instantiation	114, 105, 101	⊢
	: , : , :
67	instantiation	78, 79, 80	⊢
	: , :
68	instantiation	86, 107, 90	⊢
	: , : , : , : , :
69	instantiation	114, 82, 81	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
71	instantiation	114, 82, 83	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
73	instantiation	114, 84, 85	⊢
	: , : , :
74	instantiation	86, 87, 113, 88, 89, 90	⊢
	: , : , : , : , :
75	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
76	instantiation	114, 91, 104	⊢
	: , : , :
77	instantiation	114, 91, 102	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
79	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
80	instantiation	92, 106, 93	⊢
	: , :
81	instantiation	114, 95, 94	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
83	instantiation	114, 95, 96	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
85	instantiation	114, 97, 98	⊢
	: , : , :
86	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
87	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
88	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
89	instantiation	99	⊢
	: , :
90	assumption		⊢
91	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
92	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
93	instantiation	100, 101	⊢
	:
94	instantiation	114, 103, 102	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
96	instantiation	114, 103, 104	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
98	instantiation	114, 105, 106	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
100	theorem		⊢
	proveit.numbers.negation.int_closure
101	instantiation	114, 112, 107	⊢
	: , : , :
102	instantiation	108, 113, 111	⊢
	: , :
103	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
104	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
106	instantiation	109, 110, 111	⊢
	: , :
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
108	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
109	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
110	instantiation	114, 112, 113	⊢
	: , : , :
111	instantiation	114, 115, 116	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
114	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
115	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
116	assumption		⊢
*equality replacement requirements