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	⊢
	: , :
1	theorem		⊢
	proveit.logic.booleans.implication.iff_intro
2	deduction	4	⊢
3	deduction	5	⊢
4	instantiation	10, 15, 6, 7, 8, 9	⊢
	: , :
5	instantiation	10, 11, 12, 87, 81, 13, 14	,  ⊢
	: , :
6	instantiation	23	⊢
	: , : , :
7	instantiation	99, 100, 15, 101, 16, 18	⊢
	: , : , : , : , :
8	instantiation	99, 120, 126, 17, 18	⊢
	: , : , : , : , :
9	instantiation	99, 126, 120, 20, 18	⊢
	: , : , : , : , :
10	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
12	instantiation	19	⊢
	: , : , : , :
13	instantiation	99, 126, 100, 20, 101, 103	⊢
	: , : , : , : , :
14	instantiation	21, 51, 68, 87, 22	,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
16	instantiation	23	⊢
	: , : , :
17	instantiation	112	⊢
	: , :
18	assumption		⊢
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
20	instantiation	112	⊢
	: , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
22	instantiation	24, 25, 26	,  ⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
24	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
25	instantiation	41, 98, 51, 42, 27, 45, 28*, 46*	,  ⊢
	: , : , :
26	instantiation	29, 30, 31	,  ⊢
	: , : , :
27	instantiation	32, 92, 93, 81	,  ⊢
	: , : , :
28	instantiation	33, 86, 65	⊢
	:
29	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
30	instantiation	34, 35, 36	,  ⊢
	: , : , :
31	instantiation	37, 68, 38, 51, 39, 40*	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
33	theorem		⊢
	proveit.numbers.division.frac_zero_numer
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	41, 98, 42, 43, 44, 45, 46*	,  ⊢
	: , : , :
36	instantiation	47, 86, 56, 65, 48*	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
38	instantiation	49, 52	⊢
	:
39	instantiation	50, 51, 52, 53, 54*	⊢
	: , :
40	instantiation	55, 56	⊢
	:
41	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
42	instantiation	127, 110, 57	,  ⊢
	: , : , :
43	instantiation	127, 110, 58	⊢
	: , : , :
44	instantiation	59, 92, 93, 81	,  ⊢
	: , : , :
45	instantiation	60, 115	⊢
	:
46	instantiation	61, 62, 63	,  ⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
48	instantiation	64, 86, 65	⊢
	:
49	theorem		⊢
	proveit.numbers.negation.real_closure
50	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
52	instantiation	127, 110, 66	⊢
	: , : , :
53	instantiation	67, 78	⊢
	:
54	theorem		⊢
	proveit.numbers.negation.negated_zero
55	theorem		⊢
	proveit.numbers.addition.elim_zero_right
56	instantiation	127, 97, 68	⊢
	: , : , :
57	instantiation	127, 118, 69	,  ⊢
	: , : , :
58	instantiation	127, 118, 93	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
60	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
61	axiom		⊢
	proveit.logic.equality.equals_transitivity
62	instantiation	70, 71, 72, 75, 73*	,  ⊢
	: , : , :
63	instantiation	74, 75	⊢
	:
64	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
65	instantiation	76, 115	⊢
	:
66	instantiation	127, 77, 78	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
68	instantiation	127, 110, 79	⊢
	: , : , :
69	instantiation	127, 80, 81	,  ⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.division.frac_cancel_left
71	instantiation	127, 83, 82	⊢
	: , : , :
72	instantiation	127, 83, 84	⊢
	: , : , :
73	instantiation	85, 86	⊢
	:
74	theorem		⊢
	proveit.numbers.division.frac_one_denom
75	instantiation	127, 97, 87	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
77	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
78	instantiation	88, 89, 90	⊢
	: , :
79	instantiation	127, 118, 114	⊢
	: , : , :
80	instantiation	91, 92, 93	⊢
	: , :
81	instantiation	99, 120, 103	⊢
	: , : , : , : , :
82	instantiation	127, 95, 94	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
84	instantiation	127, 95, 96	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
86	instantiation	127, 97, 98	⊢
	: , : , :
87	instantiation	99, 100, 126, 101, 102, 103	⊢
	: , : , : , : , :
88	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
89	instantiation	127, 104, 117	⊢
	: , : , :
90	instantiation	127, 104, 115	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
92	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
93	instantiation	105, 119, 106	⊢
	: , :
94	instantiation	127, 108, 107	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
96	instantiation	127, 108, 109	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
98	instantiation	127, 110, 111	⊢
	: , : , :
99	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
100	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
101	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
102	instantiation	112	⊢
	: , :
103	assumption		⊢
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
105	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
106	instantiation	113, 114	⊢
	:
107	instantiation	127, 116, 115	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
109	instantiation	127, 116, 117	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
111	instantiation	127, 118, 119	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
113	theorem		⊢
	proveit.numbers.negation.int_closure
114	instantiation	127, 125, 120	⊢
	: , : , :
115	instantiation	121, 126, 124	⊢
	: , :
116	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
117	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
119	instantiation	122, 123, 124	⊢
	: , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
121	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
122	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
123	instantiation	127, 125, 126	⊢
	: , : , :
124	instantiation	127, 128, 129	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
126	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
127	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
128	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
129	assumption		⊢
*equality replacement requirements