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	modus ponens	1, 2	⊢
1	instantiation	3, 4	⊢
	: , : , : , : , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
5	instantiation	6, 7	⊢
	: , : , :
6	axiom		⊢
	proveit.core_expr_types.conditionals.condition_replacement
7	instantiation	8, 9, 10	⊢
	: , :
8	theorem		⊢
	proveit.logic.booleans.implication.iff_intro
9	deduction	11	⊢
10	deduction	12	⊢
11	instantiation	17, 22, 13, 14, 15, 16	⊢
	: , :
12	instantiation	17, 18, 19, 94, 88, 20, 21	,  ⊢
	: , :
13	instantiation	30	⊢
	: , : , :
14	instantiation	106, 107, 22, 108, 23, 25	⊢
	: , : , : , : , :
15	instantiation	106, 127, 133, 24, 25	⊢
	: , : , : , : , :
16	instantiation	106, 133, 127, 27, 25	⊢
	: , : , : , : , :
17	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
19	instantiation	26	⊢
	: , : , : , :
20	instantiation	106, 133, 107, 27, 108, 110	⊢
	: , : , : , : , :
21	instantiation	28, 58, 75, 94, 29	,  ⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
23	instantiation	30	⊢
	: , : , :
24	instantiation	119	⊢
	: , :
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
27	instantiation	119	⊢
	: , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
29	instantiation	31, 32, 33	,  ⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
31	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
32	instantiation	48, 105, 58, 49, 34, 52, 35*, 53*	,  ⊢
	: , : , :
33	instantiation	36, 37, 38	,  ⊢
	: , : , :
34	instantiation	39, 99, 100, 88	,  ⊢
	: , : , :
35	instantiation	40, 93, 72	⊢
	:
36	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
37	instantiation	41, 42, 43	,  ⊢
	: , : , :
38	instantiation	44, 75, 45, 58, 46, 47*	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
40	theorem		⊢
	proveit.numbers.division.frac_zero_numer
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	48, 105, 49, 50, 51, 52, 53*	,  ⊢
	: , : , :
43	instantiation	54, 93, 63, 72, 55*	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
45	instantiation	56, 59	⊢
	:
46	instantiation	57, 58, 59, 60, 61*	⊢
	: , :
47	instantiation	62, 63	⊢
	:
48	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
49	instantiation	134, 117, 64	,  ⊢
	: , : , :
50	instantiation	134, 117, 65	⊢
	: , : , :
51	instantiation	66, 99, 100, 88	,  ⊢
	: , : , :
52	instantiation	67, 122	⊢
	:
53	instantiation	68, 69, 70	,  ⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
55	instantiation	71, 93, 72	⊢
	:
56	theorem		⊢
	proveit.numbers.negation.real_closure
57	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
59	instantiation	134, 117, 73	⊢
	: , : , :
60	instantiation	74, 85	⊢
	:
61	theorem		⊢
	proveit.numbers.negation.negated_zero
62	theorem		⊢
	proveit.numbers.addition.elim_zero_right
63	instantiation	134, 104, 75	⊢
	: , : , :
64	instantiation	134, 125, 76	,  ⊢
	: , : , :
65	instantiation	134, 125, 100	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
68	axiom		⊢
	proveit.logic.equality.equals_transitivity
69	instantiation	77, 78, 79, 82, 80*	,  ⊢
	: , : , :
70	instantiation	81, 82	⊢
	:
71	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
72	instantiation	83, 122	⊢
	:
73	instantiation	134, 84, 85	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
75	instantiation	134, 117, 86	⊢
	: , : , :
76	instantiation	134, 87, 88	,  ⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.division.frac_cancel_left
78	instantiation	134, 90, 89	⊢
	: , : , :
79	instantiation	134, 90, 91	⊢
	: , : , :
80	instantiation	92, 93	⊢
	:
81	theorem		⊢
	proveit.numbers.division.frac_one_denom
82	instantiation	134, 104, 94	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
85	instantiation	95, 96, 97	⊢
	: , :
86	instantiation	134, 125, 121	⊢
	: , : , :
87	instantiation	98, 99, 100	⊢
	: , :
88	instantiation	106, 127, 110	⊢
	: , : , : , : , :
89	instantiation	134, 102, 101	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
91	instantiation	134, 102, 103	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
93	instantiation	134, 104, 105	⊢
	: , : , :
94	instantiation	106, 107, 133, 108, 109, 110	⊢
	: , : , : , : , :
95	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
96	instantiation	134, 111, 124	⊢
	: , : , :
97	instantiation	134, 111, 122	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
99	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
100	instantiation	112, 126, 113	⊢
	: , :
101	instantiation	134, 115, 114	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
103	instantiation	134, 115, 116	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
105	instantiation	134, 117, 118	⊢
	: , : , :
106	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
107	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
108	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
109	instantiation	119	⊢
	: , :
110	assumption		⊢
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
112	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
113	instantiation	120, 121	⊢
	:
114	instantiation	134, 123, 122	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
116	instantiation	134, 123, 124	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
118	instantiation	134, 125, 126	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
120	theorem		⊢
	proveit.numbers.negation.int_closure
121	instantiation	134, 132, 127	⊢
	: , : , :
122	instantiation	128, 133, 131	⊢
	: , :
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
126	instantiation	129, 130, 131	⊢
	: , :
127	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
128	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
129	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
130	instantiation	134, 132, 133	⊢
	: , : , :
131	instantiation	134, 135, 136	⊢
	: , : , :
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
133	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
134	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
135	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
136	assumption		⊢
*equality replacement requirements