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