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*	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	modus ponens	5, 6	⊢
3	instantiation	7, 141	⊢
	: , :
4	instantiation	7, 141	⊢
	: , :
5	instantiation	8, 9	⊢
	: , : , : , : , : , : , :
6	generalization	10	⊢
7	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
8	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
10	instantiation	11, 12	⊢
	: , : , :
11	axiom		⊢
	proveit.core_expr_types.conditionals.condition_replacement
12	instantiation	13, 14, 15	⊢
	: , :
13	theorem		⊢
	proveit.logic.booleans.implication.iff_intro
14	deduction	16	⊢
15	deduction	17	⊢
16	instantiation	22, 27, 18, 19, 20, 21	⊢
	: , :
17	instantiation	22, 23, 24, 99, 93, 25, 26	,  ⊢
	: , :
18	instantiation	35	⊢
	: , : , :
19	instantiation	111, 112, 27, 113, 28, 30	⊢
	: , : , : , : , :
20	instantiation	111, 132, 138, 29, 30	⊢
	: , : , : , : , :
21	instantiation	111, 138, 132, 32, 30	⊢
	: , : , : , : , :
22	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
24	instantiation	31	⊢
	: , : , : , :
25	instantiation	111, 138, 112, 32, 113, 115	⊢
	: , : , : , : , :
26	instantiation	33, 63, 80, 99, 34	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
28	instantiation	35	⊢
	: , : , :
29	instantiation	124	⊢
	: , :
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
32	instantiation	124	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
34	instantiation	36, 37, 38	,  ⊢
	: , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
36	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
37	instantiation	53, 110, 63, 54, 39, 57, 40*, 58*	,  ⊢
	: , : , :
38	instantiation	41, 42, 43	,  ⊢
	: , : , :
39	instantiation	44, 104, 105, 93	,  ⊢
	: , : , :
40	instantiation	45, 98, 77	⊢
	:
41	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
42	instantiation	46, 47, 48	,  ⊢
	: , : , :
43	instantiation	49, 80, 50, 63, 51, 52*	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
45	theorem		⊢
	proveit.numbers.division.frac_zero_numer
46	theorem		⊢
	proveit.logic.equality.sub_right_side_into
47	instantiation	53, 110, 54, 55, 56, 57, 58*	,  ⊢
	: , : , :
48	instantiation	59, 98, 68, 77, 60*	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
50	instantiation	61, 64	⊢
	:
51	instantiation	62, 63, 64, 65, 66*	⊢
	: , :
52	instantiation	67, 68	⊢
	:
53	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
54	instantiation	139, 122, 69	,  ⊢
	: , : , :
55	instantiation	139, 122, 70	⊢
	: , : , :
56	instantiation	71, 104, 105, 93	,  ⊢
	: , : , :
57	instantiation	72, 127	⊢
	:
58	instantiation	73, 74, 75	,  ⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
60	instantiation	76, 98, 77	⊢
	:
61	theorem		⊢
	proveit.numbers.negation.real_closure
62	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
64	instantiation	139, 122, 78	⊢
	: , : , :
65	instantiation	79, 90	⊢
	:
66	theorem		⊢
	proveit.numbers.negation.negated_zero
67	theorem		⊢
	proveit.numbers.addition.elim_zero_right
68	instantiation	139, 109, 80	⊢
	: , : , :
69	instantiation	139, 130, 81	,  ⊢
	: , : , :
70	instantiation	139, 130, 105	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
72	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
73	axiom		⊢
	proveit.logic.equality.equals_transitivity
74	instantiation	82, 83, 84, 87, 85*	,  ⊢
	: , : , :
75	instantiation	86, 87	⊢
	:
76	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
77	instantiation	88, 127	⊢
	:
78	instantiation	139, 89, 90	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
80	instantiation	139, 122, 91	⊢
	: , : , :
81	instantiation	139, 92, 93	,  ⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.division.frac_cancel_left
83	instantiation	139, 95, 94	⊢
	: , : , :
84	instantiation	139, 95, 96	⊢
	: , : , :
85	instantiation	97, 98	⊢
	:
86	theorem		⊢
	proveit.numbers.division.frac_one_denom
87	instantiation	139, 109, 99	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
90	instantiation	100, 101, 102	⊢
	: , :
91	instantiation	139, 130, 126	⊢
	: , : , :
92	instantiation	103, 104, 105	⊢
	: , :
93	instantiation	111, 132, 115	⊢
	: , : , : , : , :
94	instantiation	139, 107, 106	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
96	instantiation	139, 107, 108	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
98	instantiation	139, 109, 110	⊢
	: , : , :
99	instantiation	111, 112, 138, 113, 114, 115	⊢
	: , : , : , : , :
100	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
101	instantiation	139, 116, 129	⊢
	: , : , :
102	instantiation	139, 116, 127	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
104	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
105	instantiation	117, 131, 118	⊢
	: , :
106	instantiation	139, 120, 119	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
108	instantiation	139, 120, 121	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
110	instantiation	139, 122, 123	⊢
	: , : , :
111	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
112	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
113	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
114	instantiation	124	⊢
	: , :
115	assumption		⊢
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
117	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
118	instantiation	125, 126	⊢
	:
119	instantiation	139, 128, 127	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
121	instantiation	139, 128, 129	⊢
	: , : , :
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
123	instantiation	139, 130, 131	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
125	theorem		⊢
	proveit.numbers.negation.int_closure
126	instantiation	139, 137, 132	⊢
	: , : , :
127	instantiation	133, 138, 136	⊢
	: , :
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
131	instantiation	134, 135, 136	⊢
	: , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
133	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
134	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
135	instantiation	139, 137, 138	⊢
	: , : , :
136	instantiation	139, 140, 141	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
139	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
140	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
141	assumption		⊢
*equality replacement requirements