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.logic.booleans.conjunction.and_if_all
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
3	instantiation	8	⊢
	: , : , : , :
4	reference	75	⊢
5	reference	69	⊢
6	instantiation	87, 114, 88, 9, 89, 91	⊢
	: , : , : , : , :
7	instantiation	10, 39, 56, 75, 11	,  ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
9	instantiation	100	⊢
	: , :
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
11	instantiation	12, 13, 14	,  ⊢
	: , :
12	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
13	instantiation	29, 86, 39, 30, 15, 33, 16*, 34*	,  ⊢
	: , : , :
14	instantiation	17, 18, 19	,  ⊢
	: , : , :
15	instantiation	20, 80, 81, 69	,  ⊢
	: , : , :
16	instantiation	21, 74, 53	⊢
	:
17	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
18	instantiation	22, 23, 24	,  ⊢
	: , : , :
19	instantiation	25, 56, 26, 39, 27, 28*	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
21	theorem		⊢
	proveit.numbers.division.frac_zero_numer
22	theorem		⊢
	proveit.logic.equality.sub_right_side_into
23	instantiation	29, 86, 30, 31, 32, 33, 34*	,  ⊢
	: , : , :
24	instantiation	35, 74, 44, 53, 36*	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
26	instantiation	37, 40	⊢
	:
27	instantiation	38, 39, 40, 41, 42*	⊢
	: , :
28	instantiation	43, 44	⊢
	:
29	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
30	instantiation	115, 98, 45	,  ⊢
	: , : , :
31	instantiation	115, 98, 46	⊢
	: , : , :
32	instantiation	47, 80, 81, 69	,  ⊢
	: , : , :
33	instantiation	48, 103	⊢
	:
34	instantiation	49, 50, 51	,  ⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
36	instantiation	52, 74, 53	⊢
	:
37	theorem		⊢
	proveit.numbers.negation.real_closure
38	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	instantiation	115, 98, 54	⊢
	: , : , :
41	instantiation	55, 66	⊢
	:
42	theorem		⊢
	proveit.numbers.negation.negated_zero
43	theorem		⊢
	proveit.numbers.addition.elim_zero_right
44	instantiation	115, 85, 56	⊢
	: , : , :
45	instantiation	115, 106, 57	,  ⊢
	: , : , :
46	instantiation	115, 106, 81	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
48	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	58, 59, 60, 63, 61*	,  ⊢
	: , : , :
51	instantiation	62, 63	⊢
	:
52	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
53	instantiation	64, 103	⊢
	:
54	instantiation	115, 65, 66	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
56	instantiation	115, 98, 67	⊢
	: , : , :
57	instantiation	115, 68, 69	,  ⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.division.frac_cancel_left
59	instantiation	115, 71, 70	⊢
	: , : , :
60	instantiation	115, 71, 72	⊢
	: , : , :
61	instantiation	73, 74	⊢
	:
62	theorem		⊢
	proveit.numbers.division.frac_one_denom
63	instantiation	115, 85, 75	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
66	instantiation	76, 77, 78	⊢
	: , :
67	instantiation	115, 106, 102	⊢
	: , : , :
68	instantiation	79, 80, 81	⊢
	: , :
69	instantiation	87, 108, 91	⊢
	: , : , : , : , :
70	instantiation	115, 83, 82	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
72	instantiation	115, 83, 84	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
74	instantiation	115, 85, 86	⊢
	: , : , :
75	instantiation	87, 88, 114, 89, 90, 91	⊢
	: , : , : , : , :
76	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
77	instantiation	115, 92, 105	⊢
	: , : , :
78	instantiation	115, 92, 103	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
80	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
81	instantiation	93, 107, 94	⊢
	: , :
82	instantiation	115, 96, 95	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
84	instantiation	115, 96, 97	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
86	instantiation	115, 98, 99	⊢
	: , : , :
87	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
88	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
89	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
90	instantiation	100	⊢
	: , :
91	assumption		⊢
92	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
93	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
94	instantiation	101, 102	⊢
	:
95	instantiation	115, 104, 103	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
97	instantiation	115, 104, 105	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
99	instantiation	115, 106, 107	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
101	theorem		⊢
	proveit.numbers.negation.int_closure
102	instantiation	115, 113, 108	⊢
	: , : , :
103	instantiation	109, 114, 112	⊢
	: , :
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
105	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
106	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
107	instantiation	110, 111, 112	⊢
	: , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
109	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
110	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
111	instantiation	115, 113, 114	⊢
	: , : , :
112	instantiation	115, 116, 117	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
114	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
115	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
116	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
117	assumption		⊢
*equality replacement requirements