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	⊢
	: , : , :
1	reference	73	⊢
2	instantiation	3, 35, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
4	instantiation	75, 7, 100, 9	⊢
	: , : , : , :
5	instantiation	75, 8, 100, 9	⊢
	: , : , : , :
6	instantiation	10, 11, 12	⊢
	: , : , : , :
7	instantiation	13, 14, 15, 16, 17, 18, 19, 20*	⊢
	: , : , : , :
8	instantiation	105, 21, 22	⊢
	: , : , :
9	instantiation	56, 23	⊢
	: , :
10	theorem		⊢
	proveit.core_expr_types.tuples.merge_front
11	instantiation	24, 93, 48	⊢
	: , :
12	instantiation	56, 25	⊢
	: , :
13	theorem		⊢
	proveit.core_expr_types.tuples.general_len
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
15	instantiation	104	⊢
	: , :
16	instantiation	104	⊢
	: , :
17	instantiation	104	⊢
	: , :
18	instantiation	26, 135, 43	⊢
	: , : , :
19	instantiation	105, 48, 27	⊢
	: , : , :
20	instantiation	67, 28, 29	⊢
	: , : , :
21	instantiation	30, 31	⊢
	: , : , :
22	instantiation	67, 32, 33	⊢
	: , : , :
23	instantiation	34, 35	⊢
	: , :
24	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
25	instantiation	67, 36, 37	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.sub_left_side_into
27	instantiation	75, 49, 38, 39	⊢
	: , : , : , :
28	instantiation	40, 140, 41, 42, 43, 57	⊢
	: , : , : , :
29	instantiation	67, 44, 45	⊢
	: , : , :
30	theorem		⊢
	proveit.core_expr_types.tuples.range_len
31	instantiation	46, 90, 47, 93, 48, 135	⊢
	: , :
32	instantiation	73, 49	⊢
	: , : , :
33	instantiation	75, 50, 51, 52	⊢
	: , : , : , :
34	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
35	instantiation	138, 53, 134	⊢
	: , : , :
36	instantiation	86, 93, 140, 135, 95, 54, 98, 114	⊢
	: , : , : , : , : , :
37	instantiation	92, 135, 140, 93, 55, 95, 98, 114, 112*	⊢
	: , : , : , : , : , :
38	instantiation	109	⊢
	:
39	instantiation	56, 57	⊢
	: , :
40	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
41	instantiation	104	⊢
	: , :
42	instantiation	104	⊢
	: , :
43	instantiation	58, 114, 66	⊢
	: , : , :
44	instantiation	86, 135, 140, 93, 62, 95, 114, 102, 64	⊢
	: , : , : , : , : , :
45	instantiation	59, 114, 102, 66	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.add_nat_closure
47	instantiation	103	⊢
	: , : , :
48	instantiation	60, 61	⊢
	:
49	instantiation	84, 98, 114, 85*	⊢
	: , :
50	instantiation	86, 135, 140, 62, 88, 102, 64, 114	⊢
	: , : , : , : , : , :
51	instantiation	89, 93, 90, 95, 63, 102, 64, 114	⊢
	: , : , : , :
52	instantiation	65, 114, 102, 66	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
54	instantiation	104	⊢
	: , :
55	instantiation	104	⊢
	: , :
56	theorem		⊢
	proveit.logic.equality.equals_reversal
57	instantiation	67, 68, 69	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
59	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
60	theorem		⊢
	proveit.numbers.negation.nat_closure
61	instantiation	70, 71, 72	⊢
	:
62	instantiation	104	⊢
	: , :
63	instantiation	103	⊢
	: , : , :
64	instantiation	120, 114	⊢
	:
65	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
66	instantiation	109	⊢
	:
67	axiom		⊢
	proveit.logic.equality.equals_transitivity
68	instantiation	73, 74	⊢
	: , : , :
69	instantiation	75, 76, 77, 78	⊢
	: , : , : , :
70	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
71	instantiation	79, 122, 130	⊢
	: , :
72	instantiation	80, 108, 119, 110, 81, 82*, 83*	⊢
	: , : , :
73	axiom		⊢
	proveit.logic.equality.substitution
74	instantiation	84, 98, 121, 85*	⊢
	: , :
75	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
76	instantiation	86, 135, 140, 87, 88, 102, 115, 114	⊢
	: , : , : , : , : , :
77	instantiation	89, 93, 90, 95, 91, 102, 115, 114	⊢
	: , : , : , :
78	instantiation	92, 135, 140, 93, 94, 95, 102, 115, 114, 96*	⊢
	: , : , : , : , : , :
79	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
80	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
81	instantiation	97, 134	⊢
	:
82	instantiation	113, 114, 98	⊢
	: , :
83	instantiation	99, 102, 100	⊢
	: , :
84	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
85	instantiation	101, 102	⊢
	:
86	theorem		⊢
	proveit.numbers.addition.disassociation
87	instantiation	104	⊢
	: , :
88	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
89	theorem		⊢
	proveit.numbers.addition.elim_zero_any
90	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
91	instantiation	103	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.addition.association
93	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
94	instantiation	104	⊢
	: , :
95	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
96	instantiation	105, 106, 107	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
98	instantiation	138, 126, 108	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
100	instantiation	109	⊢
	:
101	theorem		⊢
	proveit.numbers.negation.double_negation
102	instantiation	138, 126, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
104	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
105	theorem		⊢
	proveit.logic.equality.sub_right_side_into
106	instantiation	111, 114, 121, 112	⊢
	: , : , :
107	instantiation	113, 114, 115	⊢
	: , :
108	instantiation	138, 131, 116	⊢
	: , : , :
109	axiom		⊢
	proveit.logic.equality.equals_reflexivity
110	instantiation	117, 118, 134	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
112	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
113	theorem		⊢
	proveit.numbers.addition.commutation
114	instantiation	138, 126, 119	⊢
	: , : , :
115	instantiation	120, 121	⊢
	:
116	instantiation	138, 136, 122	⊢
	: , : , :
117	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
118	instantiation	123, 124	⊢
	: , :
119	instantiation	138, 131, 125	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.negation.complex_closure
121	instantiation	138, 126, 127	⊢
	: , : , :
122	instantiation	128, 129	⊢
	:
123	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
125	instantiation	138, 136, 130	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
127	instantiation	138, 131, 132	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.negation.int_closure
129	instantiation	138, 133, 134	⊢
	: , : , :
130	instantiation	138, 139, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	138, 136, 137	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
134	assumption		⊢
135	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
136	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
137	instantiation	138, 139, 140	⊢
	: , : , :
138	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
139	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
140	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements